David King b. August 1, 1754/1755

My great great grandfather was David King born in Scotland. My information about his birth comes from his Revolutionary War pension statement. He says he was born in Scotland on August 1. The year could be 1754/1755.
He came to the United States just as the Rev. War was beginning and fought in both South and North Carolina. He lived in Gerogia after the War and finally settled in Mississippi by 1808.
Our family has long looked for some proof of where he was born in Scotland and who his parents were. One family located that was a possibility was George and Mary Ninian King. So far, they are just a possibility. If this is the family, there is also a possibility he had brothers John and William and a sister named Mary.
This family was located in Ayershire. Can anyone help me to find this proof or give me tips on how to prove this?
Another researcher directed me to this site. Thanks Joyce.