My 6 month old puppy has diarrhea with blood in it. He has had his vaccinations but ate some chicken skins the other night. What could be the problem?

We out here in cyberspace have no clue. Please take him to the vet!

Chicken skin wouldn't do it, but chicken bones would. Better get him to the vet if there is blood in his stool. And there were no bones in what he ate?

Vaccinations or not, bloody diarrhea warrants a visit to the vet. Intestinal parasites, ingesting something he shouldn't have, likes bones or parts from toys, Vaccinations, while they are a wonderful thing cannot guarantee 100% protection, and since I'm not sure what vaccines you are referring to, parvo may also be a possibility.
Also, make sure you are aware of other things, like appetite, nausea, attitude (playful and happy or lethargic and tired)
Just best to be safe and not sorry, take him to the vet