I would warn you NOT to flush any litter, even if it's touted as flushable. I clogged my pipes with Feline Pine.
Your best bet is to pick up the poop with a baggie and trash it. Yes, the pellets stick to the poop, but don't completely cover it like clay litter does.
Is pine litter what your breeder has been using? My ragdoll kit was using Feline Pine at the breeders, and as soon as he had a choice to use that or my other cat's scoopable clay, he stopped using the pine. That was fine by me, I didn't like that stuff.