There is quite a bit in the New England Hist. & Genealogical Register for the ancestry of Samuel HINCKLEY. Their migration record from the Kent Archives Office: SA/ZB/2 was published in Peter Wilson Coldham's Complete Book of Emigrants, 1607 - 1660. Embarked in the Hercules, of Sandwich, Kent, Mr. John Witherley (captain), to be transported from Sandwich to New England, April 1635...Samuel Hinckley of Tenterden and Sara his wife, ch. Susan, Sara, & Mary, & kinswoman, Elizabeth Hinckle.
I do not know for whom the city of Hinckley was named, but there's probably a connection. Have you checked whether there is a Hinckley DNA project at FamilyTreeDNA? My brother sent his test kit there for our Green surname but didn't find any match with the name Green. We're Haplogroup R1b1b2, very northern European. For mtDNA, we're descendants of Hannah.