First, you would want to include an article:
He really killed the fried chicken.
Second, you are correct – either meaning is possible, and more context would help us determine which meaning is intended. Consider:
He killed a whole bucket of Kentucky Fried Chicken! Amazing!
I'd assume that meant eating the whole thing (probably in one sitting). However:
He killed that fried chicken last night. It was delicious!
I'd assume that referred to how well the chicken was prepared.
Third, you should realize this is a very informal use of the verb kill, and that word has other slang meanings as well. In addition to the two meanings you list here, it can also mean to ruin:
He killed that fried chicken last night. We had to go out to eat instead.
Fourth, absent any further context, the original sentence could mean that he literally butchered the chickens:
He really killed the fried chicken!
What, do you mean he cooked it well?
No, I mean he really killed it! Some friend of his has a chicken farm about 30 miles from town – we went there last weekend and killed three birds.