I am not an advocate of mixing fowl. The turkeys grow big and fast and will out grow your chickens. They will also pick on the chickens alot and can hurt them due to their size dominance. I like everything nice and tidy living in their own coops and runs.
How big is your pen? I would mostly be worried about the turkeys jumping on the chickens when they fly down from the perches. A few turkeys in with chickens are usually not a problem, but I'm not sure about having that many in with the chickens. I have three mixed in with a flock of chickens, but they get plenty of free range time.
If you have a lot of space in your coop, you might be ok. If it's going to be cramped, I'd say just build a new coop and run for them instead of taking the chance you might lose birds. If you are only planing to keep a few, you should be fine mixing them. Generally, the turkeys and chickens rarely bother with each other.
I have never had a problem with diseases spreading from my turkeys to my chickens, but I have read plenty about it. It would be hard to prevent some of those diseases from occurring if the two types of poultry are in the same yard, or next to each other. So either if you mix them or if you don't, there is still a chance of birds getting sick. THe only way to fully prevent disease is through super bio security, and even that is not fail safe.