Ahh yes, the joys of irrigation.
If you can't actually get the syringe tip in to flush it out, make sure to keep it from scabbing over and do your best to flush the outside to encourage free drainage without gunk build up around the edges.
Body temp. Solution helps as does holding a clean cloth dipped into the flushing solution just over the hole. It softens the build up and makes the wound feel better.
Sometimes if the horse realizes you are just going to hold a warm rag on the outside he will relax a bit and not really feel it if you sneak the syringe close enough to squirt a little into it.
I'm sure the vet showed you how to really "flush" it out forcefully, but as one who has had that treatment myself... it feels weird! (I didn't have an abcess.. deep wounds and surgery with with penrose drains.)
Perhaps more gentle squirts after the warm rag will help him stay relaxed.
Maybe some favorite treats for distraction too.
Fun ain't it?