I've often heard from others that the first man in the British colonies of North America to possess as permanent property a black African was a black planter named Anthony Johnson. Is there any validity to this claim?
Not really, this is a pretty common talking point among Neo-Confederates and the Lost Cause school of revisionism. Unsurprisingly, it's wrong. It's not even true of the Virginia colony. The first documented instance of a person being declared a slave in Virginia is the John Punch case in 1640. Punch was given a lifelong indenture as punishment for having escaped along with two other (white) servants, who saw finite extensions of their indentures—in turn making this the first documented case drawing a racial distinction being made with reference to compulsory servitude.
The significance of the Johnson case (1655) is that it was the first instance of a person being declared a slave as a result of a civil suit, and is established precedent for a free black persons to own slaves.
I realize that there isn't a whole lot of depth to this comment, but there's not much required to refute that claim.