Hi
Maybe just flush it with a sterile saline solution. My vet once told me that using a trigger sprayer to irrigate wounds is really good because the pressure of liquid hitting the site helps to get into any pockets and flush out debris/anything bad without the scrubbing action on the damaged tissue associated with conventional cleaning with a dressing. Certainly works great for horses wounds although I've always used diluted Chlorohexidine in the spray bottle.
As regards trying to draw the abscess, I understand that puss in chickens is not liquid like you would expect but a cheesy textured solid, so s needle wouldn't draw it out. Probably better to cut it open and physically remove like you would with bumblefoot, but see how you go with the antibiotics first.
Fingers crossed the antibiotics help and I would have some probiotics ready to give him once the course is finished... or fermented feed.... to help his gut get back to normal.
Best wishes
Barbara