***it all depends on the individual birds, but, generally there are some recipes for disaster.
I've never had a tom rape chickens before. One young guy occasionally looks like he's courting a BO pullet here, but his girl has been broody a long time. His dad stomped a poult to death attempting to mate it, but once he had adult lady company, you couldn't hope to find a better dad among the species.
Fireworks happen when certain birds meet sometimes. Worst fights between turkeys and chickens, in my experience, is when a young rooster thinks he's hot stuff and doesn't bow out of the way to the turkey train. Turkey hens will generally peck other hens and may stomp the life out of persistent roosters (only seen that once, but I have seen roosters who might have been seriously injured without some caring intervention). I've never had a rooster willing to seriously take on a tom, but for some reason, they're sometimes stupid enough to try hens.
So long as sane, healthy genetically sound turkeys have ample companionship of their own species in a nice female-heavy ratio and plenty of room and protein in their diet, you shouldn't have any problems with them coexisting with chickens and other fowl. All of the problems I've seen boil down to something wrong with the above recipe. I mention "sane" because I've seen and heard of birds acting really out of character due to various infections, leg mites driving them crazy, isolation, sexual deprivation, etc.
Also beware of problems with imprinting because turkeys just don't seem to shrug off parental effects the way other species do. Turkeys get and stay pretty confused about species boundaries and may try on humans, dogs and other species if imprinted on them
Most turkeys are just fine with chickens and never have any serious issues with them--even if they're the only turkey in the group.