Turkeys can get blackhead from chickens, however, contact your local ag vet or poultry sci specialist and they can tell you if it is even a concern in your area. Speaking with a poultry sci vet, I have learned blackhead is not a problem where I live in the pacific north west, so there is no risk in keeping the turkeys and chickens together.
PC, with that many birds, I'd keep them all in their own digs. Ducks will make a mess of the place with the water which would turn the ground into cocci breeding central and risk the chickens and turkeys. The chickens and turkeys are usually put on something like 20 percent and 28 percent protein feed respectively, so that may be an issue if you had those together.
However, I raised 8 cornish x, and two broad breasted bronze turkeys together for a while on turkey starter. Surprisingly, the cornish x put on weight faster than the turkeys did for the first 5-6 weeks and when they ranged together with the dust bunny looking silkie chicks the same age, they all got along just fine. After the cornish x were eaten up, the turkeys kept on hanging out with the silkies and were nice enough to be a living perch for the orange balls of fluff. The turkeys really started putting on weight in the last two months of their 5 month long life. At the end, they were putting on about 1-2 lbs a week! All said and done, I had a 30 and 33lb turkey for the oven. Hard to weigh alive, but they were about 40lbs at 5 months and 5.5 months old. They had a TON of blood. So much I caught and weighed it from the second turkey and it was over a lb! Had I thought ahead, I could have put that blood to good use instead of throwing it away.