I am a direct descendant of Thomas Drake, one of the brothers of Sir Francis. Thomas sailed with his famous brother and inherited most of his estate. Thomas' son, Francis, inherited the title, Sir Francis Drake.
There is a wealth of info available on most of the descendants of Thomas' parents, Edmund Drake and Elizabeth Hawkins, and I've gotten a great deal of info for my tree from others on the genealogy forum. You may also find a lot of the family tree indicated in "Visitations of the County Devon" and "Historical Southern Families, vol. VII" at your local library.
I have my own tree back through 12 generations to Edmund. I am still looking for more information about my Benjamin Drake, who was born on 6/10/1742 in Loudon County, Virginia.
It all takes time. I've been at it for about ten years.