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Okay, so no visible lesions, sores, etc? If they are just eating poop in his litter box, then it isn’t a huge deal. You’ll want to try to get rid of them though because you don’t want them to move from his poop to his rear. Most of the time they are only attracted to a dirty bottom, but it’s still good to be safe.
Intestinal myiasis is very rare and happens when someone eats food contaminated with fly eggs/larva. I don’t know of any documented cases in rabbits. I did a search and all I could find were some experiments done in the 1930s where they (unsuccessfully) tried to cause intestinal myiasis in rabbits by feeding them fly larva. Yikes! Anyway, my point is that it is unlikely your bunny has them in his intestines. I imagine he would be exhibiting other gastrointestinal symptoms if he did.
Flies don’t care if a house is clean or dirty, so don’t beat yourself up. Are you in a warmer climate where flies would be active year round? Really, it only takes one fly to come in and find your bunny’s litter box. Hopefully you can figure out where the flies are coming from. In the meantime, you could hang fly tape from the ceiling to try to catch any little buggers flying around.