The flock is mixed, dominique, EE, RIR, Black Astro, RLBW, LB.
I'll add a bit that may not help you much but then it might. I don't know what an LB is and EE's can be any color or pattern. So I can't tell what the chicks would look like from those hens. But with the others, the Dominique should give you black barred chicks. Some may have that scattered Cuckoo pattern like the Dominique and some may have the sharp barring of the Barred Rock but all his offspring with those other hens should be black barred. The others probably will too, I just don't know what they look like. The Dominique has a rose comb which is dominant so all the chicks will have a rose comb except maybe the EE and LB. If the EE hens have a pea comb those chicks could have a walnut comb.
Your EE boy is mainly red and looks like he has a pea comb. Not sure if he s pure for that Pea Comb gene or not which leaves some uncertainty about his chicks' combs. Since EE's are often mixed in colors/patterns you don't know what else genetically he may be carrying so you can get surprises. You will get more variety with his chicks. He may or may not be carrying the blue egg gene. Since he is a rooster that does not lay eggs you just don't know for sure but there is a chance you could get a bunch of blue or green eggs from his pullets. There is some guessing involved since you don't know how he may be crossed, but if you cross him with
Dominique - You should get a walnut combed black barred chick. These should be black sex links but only if you know which eggs came from the Dominique hens.
RIR - Red chicks.
Black Australorp - You should get solid black chicks.
Wyandotte - Red chicks that should feather out with lacing. Probably walnut combs.
EE and LB - I don't know what the hens look like.
In general a Black or Black Barred rooster has chicks that look a lot like him. Barring is dominant, black overwhelms most other colors. A Red rooster has less influence on what his chicks looks like, the hen has a lot more influence.
I see that the myth that there is something mystical and magical about hen to rooster ratio has come up. There is not anything magical about it. Many of us have experience that shows (at least to us) that you can have the same issues whether you have one rooster with 2 or 3 hens or one rooster with 25 or 30 hens. Or you may have no issues. There are other things that are much more important than that ratio including the personality of the girls and boys involved, how much room you have, and age. Adolescence can be rough. But once a myth gets started it never dies. You'll read about that ratio all over this forum.
What are you goals with your chickens? How does a boy fit into those goals. The only reason you need a rooster is if you want fertile eggs. Anything else is personal preference. Nothing wrong with personal preferences, I have a few of my own. I generally recommend that you keep as few boys as you can and still meet your goals. That's not because you are guaranteed more problems if you have more boys but ore problems are certainly more likely.
You said you want to keep one and it sounds like you do want fertile eggs, that's why I went through all that above. I don't know how much the color of the chicks or possible color of the eggs will influence you. It can be very challenging to select a cockerel based on behaviors. That's one of my criteria and I don't always get it right. They mature at different rates. When they are immature cockerels and the hormones hit they just don't have much (if any) self control when it comes to the girls. The competition between the two may make them a lot more active than they would be on their own. Or a dominant one may repress the not-dominant one's actions. The girls can have some influence on this too, they have their own personalities. When they all mature things usually calm down a lot but getting through puberty can be hard to watch.
I think getting down to one boy is the right choice for you. I don't know which one though. That will depend a lot on your personal preferences, not mine. Holding off on making that decision is probably a good thing but I don't think you can ever be absolutely sure. They influence each other too much and their behaviors can change as they mature, not always for the good.
I suggest having some place ready to immediately separate them from each other or the flock if the need arises. That need could happen at the drop of a hat.
Good luck with it. Deciding which boy to keep is a much harder decision for me than deciding which girls to keep.
I'll add a bit that may not help you much but then it might. I don't know what an LB is and EE's can be any color or pattern. So I can't tell what the chicks would look like from those hens. But with the others, the Dominique should give you black barred chicks. Some may have that scattered Cuckoo pattern like the Dominique and some may have the sharp barring of the Barred Rock but all his offspring with those other hens should be black barred. The others probably will too, I just don't know what they look like. The Dominique has a rose comb which is dominant so all the chicks will have a rose comb except maybe the EE and LB. If the EE hens have a pea comb those chicks could have a walnut comb.
Your EE boy is mainly red and looks like he has a pea comb. Not sure if he s pure for that Pea Comb gene or not which leaves some uncertainty about his chicks' combs. Since EE's are often mixed in colors/patterns you don't know what else genetically he may be carrying so you can get surprises. You will get more variety with his chicks. He may or may not be carrying the blue egg gene. Since he is a rooster that does not lay eggs you just don't know for sure but there is a chance you could get a bunch of blue or green eggs from his pullets. There is some guessing involved since you don't know how he may be crossed, but if you cross him with
Dominique - You should get a walnut combed black barred chick. These should be black sex links but only if you know which eggs came from the Dominique hens.
RIR - Red chicks.
Black Australorp - You should get solid black chicks.
Wyandotte - Red chicks that should feather out with lacing. Probably walnut combs.
EE and LB - I don't know what the hens look like.
In general a Black or Black Barred rooster has chicks that look a lot like him. Barring is dominant, black overwhelms most other colors. A Red rooster has less influence on what his chicks looks like, the hen has a lot more influence.
I see that the myth that there is something mystical and magical about hen to rooster ratio has come up. There is not anything magical about it. Many of us have experience that shows (at least to us) that you can have the same issues whether you have one rooster with 2 or 3 hens or one rooster with 25 or 30 hens. Or you may have no issues. There are other things that are much more important than that ratio including the personality of the girls and boys involved, how much room you have, and age. Adolescence can be rough. But once a myth gets started it never dies. You'll read about that ratio all over this forum.
What are you goals with your chickens? How does a boy fit into those goals. The only reason you need a rooster is if you want fertile eggs. Anything else is personal preference. Nothing wrong with personal preferences, I have a few of my own. I generally recommend that you keep as few boys as you can and still meet your goals. That's not because you are guaranteed more problems if you have more boys but ore problems are certainly more likely.
You said you want to keep one and it sounds like you do want fertile eggs, that's why I went through all that above. I don't know how much the color of the chicks or possible color of the eggs will influence you. It can be very challenging to select a cockerel based on behaviors. That's one of my criteria and I don't always get it right. They mature at different rates. When they are immature cockerels and the hormones hit they just don't have much (if any) self control when it comes to the girls. The competition between the two may make them a lot more active than they would be on their own. Or a dominant one may repress the not-dominant one's actions. The girls can have some influence on this too, they have their own personalities. When they all mature things usually calm down a lot but getting through puberty can be hard to watch.
I think getting down to one boy is the right choice for you. I don't know which one though. That will depend a lot on your personal preferences, not mine. Holding off on making that decision is probably a good thing but I don't think you can ever be absolutely sure. They influence each other too much and their behaviors can change as they mature, not always for the good.
I suggest having some place ready to immediately separate them from each other or the flock if the need arises. That need could happen at the drop of a hat.
Good luck with it. Deciding which boy to keep is a much harder decision for me than deciding which girls to keep.
I am sure the pandemic had something to do with it, so I refused to replace them with another shipment and just purchased from the stock at my local 
