There's some big problems with their claims. The confederacy they mention as the whole basis for their claims wasn't around for very long, and was made up of pre existing tribes. That would make them somewhat like the Seminole, except for one thing: the Seminoles' ancestors' tribes no longer existed, too shattered by warfare. All these tribes making up the Chikimaka did continue and still exist today.
So maybe their claim is that they are a mixed people of several tribes plus some whites like the Metis or even the Lumbee. Problem is, those peoples existed as a unit. Their whole claim is that the Chikamaka had to hide so deep underground that's why there's no record they can point to. That'd make them possibly descendants then. Really, how likely is there to be NO record? No churches they all went to? No influence on their dialect? No dances? No ceremony? No oral tradition beyond family stories of being part Indian? I didn't seen any of that mentioned in the search I did. If so, then that'd make them assimilated so totally as to be de facto culturally white.
Their founder James Meeks mentions in several articles being "1/3 to 1/2 Indian." 1/3?