Thanks for the update. I was concerned when you didn't come back to the thread after the syringing issue. It is great to hear the small flushing produced results.
As far as reintegration, the longer she's apart from the flock, the harder it'll be for her. Try easing her back into the flock by letting her spend time in a separate enclosure in view of the others. This is referred to many of us as the 'jail", an all-purpose enclosure to keep a chicken safe without removing them from the flock.
If you do not have such an enclosure, consider adding it to your run. You'll be very glad you did, as it can be used in a pinch for lots of things, including isolating a combative chicken, segregating a sick chicken, or even brooding baby chicks.
Or you can put her in a crate and let the others get reacquainted with her, then let her out of the crate after a few hours.
It's not necessary to immediately isolate a sick or injured chicken. Most of the time, the chicken can be treated without removing them from the flock.
Back to tube feeding. When the kit comes, measure the length of the average crop from beak to bottom of the crop and make a mark on it. It's best to have no more than four inches extending out from the beak to maintain easy control of the tubing while feeding. It it's too long, shorten it accordingly and heat the tip if it feels like it's too rough. You don't want to lacerate the crop tissue inserting it.
Then, nominate one of your more docile chickens to practice on. Just use plain warm water (all fluids or food should be around 100F so as not to chill the chicken). Have the tubing, syringe and fluids set up and ready. Have a towel to wrap the chicken in to confine wings so as to reduce flapping and resistance.
Then hold the chicken on a table or counter close to your body with your weak hand, beak facing your strong hand. Pry open the beak and hold it open with your weak hand while inserting the tubing on the right side of the beak, going along the side of the throat and slightly under the side of the tongue, aiming for the esophagus. The end of the tube should stop short of the bottom of the crop sack. This is why a make on the tube is handy.
Don't be alarmed if the chicken coughs. That is a signal you don't have the tube aimed correctly. Back it out and try again. If you feel resistance, jiggle the tubing until it slides easily into the crop. If you are doing it correctly, there will be no coughing or gagging. Never inject fluids into a coughing chicken.
The chicken may struggle a bit. Just hang on tight and keep the tube in place by closing the beak over it with the fingers of your weak hand until the chicken relaxes. Then fill the syringe and proceed inserting it into the tube and emptying it into the crop. Do not overfill the crop. Usually, you do not want to put more than half a cup of liquid into the crop of an average size chicken. Syringe slowly and avoid emptying the syringe too quickly as it can be uncomfortable. The chicken usually will relax as you tube warm fluids into her. It's a pleasant sensation as the crop fills. When finished, slowly withdraw the tubing, and you're done. Hopefully, you've gotten more into the chicken than on yourself.
Practice is advised so you will not be tense and uncertain when dealing with a very sick chicken during a life or death situation. Once you've tubed once, the next time is a walk in the park.