I have been able to give my Pets a flea bath, but I do sometimes see the action fall off the Pet's que. But that seems to happen for actions other than just the Flea bath. Sometimes, items just fall off the que.
I have noticed that sometimes, it seems like an autonomus action on the Pets part (Like the Cat grooming itself) will cause the items to drop.
I also noticed that if I regularly brush the Cat, it is less likely to scratch me when I try to bathe it.