The "thumb rules" say yes, you could increase the number of chickens, and that with a 250 sq ft run dedicated to ducks, you could have some number of them, too. Obviously, and as you have acknowledged, the coops need to be increased in size.
Now, in the case of the chicken coop and run, you could take out the tiny "dog house" coop and build a raised coop at the covered end of the run, enclosing the back wall and part of the two sides. Chickens would retain all the "floor" space, and you could go, potentially, to about 20 birds with common and reasonable management practices. You will have to go into the coop to gather eggs, which may or may not, be an attractive idea for you.
With ducks, you don't have that option. They nest on the ground, vertical space is useless to you, thus their coop cuts your floor space. For my own 8-duck design, which I found manageable, they nest under my raised hen house, and have about 100 sq ft to that purpose. While that's probably twice the usual rule of thumb (6 sq ft house per duck), I had more than one male - the extra space was absolutely needed.
My run was shared with my chickens, which makes the numbers a little squirrely, but the "thumb rule" is about 25 ft per duck, minimum. Given those things, and my experiences, in an enclosure of 250 sq ft, I'd place just 6 ducks. One drake, five hens. Or six hens. Not more than that.
Expect a lot of work, ducks are messy messy messy creatures, you will be putting a lot of effort into maintaining their run, but it can be accomplished.