Fried chicken, like most of what people in the Northeast, Midwest and West Coast associate with the category of "soul food" is actually Southern country food, and like a lot of things that are associated with black people are part of the shared cultural heritage of the rural American South. Between 1910 and 1970 there were mass migrations of black people leaving the South to get jobs in cities all over the country. They took Southern cooking, music, and other cultural identifiers with them to their new homes. The people in those areas associated southern culture with black skin because they were introduced to it by black people who had migrated from the south into their communities.
As far as why fried chicken is such a staple for soul food and southern cooking, like most of that area of cuisine it is an ingredient that is cheap and easy to produce on hot weather farms. Southerners often call chicken "yard birds" (this is where the famous white British blues rock band got their name) because a farmer can keep a small flock of chickens open range in their back yard with very little cost and effort. They can be fed in about 5 minutes, the regular feeding keeps them close to the farm so they don't require tending, they produce eggs when young and when they stop producing eggs they can be slaughtered and turned into a meal for a family.
Using the meat immediately is a big advantage in a hot weather area where meat can spoil quickly, looked at in that light it's no coincidence that the most common southern meals are fried chicken and red beans and rice made with salt pork (salting is the easiest way to preserve pork in the heat). People who grew up in the South before the 1980's ate a lot of fried chicken, and people who moved from the South took their eating habits with them.
hi! here's a similar post with some more info