The worms infecting your cats will not be the same ones in your poultry (as far as I'm aware). I believe the species need to be pretty closely related in order for the same parasite to cross species (like goats to sheep). The exception, of course, is coccidiossis which really isn't a parasite - but will jump from one flock to the next.
I'm going to put my bullet proof helmet and vest on here.... There is utterly no evidence that DE in any way prevents or controls internal parasites in animals. There is some evidence that it may hinder external parasiets. But, DE has been scientifically studied by Universities and shown to have no benefit (except to the people selling it).
I wish, I truly wish it did work, because anything organic in my book is great. But, what you ought do is save your money and do the following:
1) Collect some chicken poop.
2) Take it to your vet to do a float.
3) If parasites are identified, they will give you a prescription which works specficially for those parasites actually identified.
4) Administer the anthelmic per instructions.
DO NOT DEWORM IF NO PARASITES ARE IDENTIFIED. For the long term sustainability of your farm, prophylactically deworming is the worse thing you can ever do. It ensures the most rapid course to dealing with paraistes which are immune to deworming, and then you have a very serious issue to deal with.
The fecal float will cost less than a bag of DE. The dewormer, depending on how many animals, will cost about the same as 1-2 bags of DE. Spend your money wisely.