My opinion: questions about vermin are allowed, so long as one of the following criteria is met:
- The vermin are parasites most commonly associated with pets, and the infestation involves pet animals
- The vermin infestation involves pet animals, and any solution will have to involve specific considerations for the pets that wouldn't likely be necessary in other contexts.
So questions regarding fleas, ticks, worms, etc. would all be on topic, unless the question was about a non-pet infestation (e.g. "I have fleas", "My herd of cattle have worms" [presuming we agree that a herd of cattle does not constitute as pets], "when hunting, do I have to worry about getting intestinal parasites from eating the meat", etc.).
To me, that still leaves your question about your chickens borderline. However, your comment about poison not being an option is a good argument for my second bullet point. Given that, and John Cavan's answer on this question, I'll agree that your question should be reopened.