He isn't a Blackfyre. Blackfyre was a specific Targaryen bastard who was legitimized and given the family sword. His legitimate brother inherited but was seen as weak and allowed Dornish influence into his court. Blackfyre though of himself as the only deserving heir of his father and eventually started a rebellion with one of his other bastard brothers. They lost, their sons ran to the Free Cities, plotted a return to Westeros, started a mercenary army, etc. but eventually all of the recognized heirs to the Blackfyre bloodline died.
On the other hand, there's a quite convincing theory that Aegon
, or the Aegon we meet in ADwD, may be Blackfyre. It's noted that only the "male line" of the Blackfyres died when Barristan slew the one with the infant head on his neck. Illyrio had a Valyrian-looking wife and there's hints Aegon is Illyrio's son (the child clothes Tyrion finds, the fact that Illyrio gets, strangely to Tyrion, upset when he learns he won't be able to see Aegon off), none of which point to Blackfyre
specifically, except in conjunction with a story told in A Feast for Crows about a black dragon sign that is thrown down the river and later comes back washed up falsely looking red. Not necessarily the way it'll go down, but it's an interesting possibility.
He is a proper Targaryen, the legitimate or legitimized son of Prince Rhaegar and Lyanna. (probably)
I'd say legitimate. If he wasn't, then Hightower and the other two members of the Kingsguard would've been with Viserys. They make it quite clear to Ned that they know both Aerys and Rhaegar are dead (meaning if Rhaegar had just said, "Guard Lyanna," those orders would become moot as soon as he died and Viserys became king). The fact that they're still there, still doing their duty as they go out of their way to point out, heavily implies Jon is legitimate (and why the series stresses that Targs practice polygamy).