There absolutely is a link between inbreeding and Valyrian draconic bloodmagic:
“The tradition amongst the Targaryens had always been to marry kin to kin. Wedding brother to sister was thought to be ideal. Failing that, a girl might wed an uncle, a cousin, or a nephew; a boy, a cousin, aunt, or niece. This practice went back to Old Valyria, where it was common amongst many of the ancient families, particularly those who bred and rode dragons. “The blood of the dragon must remain pure,” the wisdom went. (emphasis mine) (WOIAF)
How this link works exactly is less clear.