I know it's not passed genetically, which is why I started to wonder how Martin used the Amulet. But if Martin was blessed by the Divines, then it makes sense. (That last part was what I was getting confused about. I thought the only two recent Dovahkiin were Tiber Septim and the PC.)
All the legitimate Septims were dragonblood, so it was likely Martin would have been able to. It seems to be a case where you know it when you see it- if they can light the Dragonfires, they're of dragon blood.
http://www.uesp.net/wiki/Lore:The_Book_of_the_Dragonborn the relevant book quote I was thinking of.
Very few realize that being Dragonborn is not a simple matter of heredity - being the blessing of Akatosh Himself, it is beyond our understanding exactly how and why it is bestowed. Those who become Emperor and light the Dragonfires are surely Dragonborn - the proof is in the wearing of the Amulet and the lighting of the Fires. But were they Dragonborn and thus able to do these things - or was the doing the sign of the blessing of Akatosh descending upon them? All that we can say is that it is both, and neither - a divine mystery.
The line of Septims have all been Dragonborn, of course, which is one reason the simplistic notion of it being hereditary has become so commonplace. But we know for certain that the early Cyrodilic rulers were not all related...