Other than someone with a natural talent for it, I think it's a side effect of lots of chess calculation/visualization practice and will naturally surface after a few years of playing regularly. I say a few years but sure it will be different for everyone.
I think the first time I successfully played a game blindfolded was after I'd been playing 5 years regularly and I was terrible at chess when I began. Among other things I remember when I worked hard on calculating 2 moves ahead to see if I'd loose my center pawn early in the opening. It was defended twice and attacked twice, I checked again just to be sure... and I was safe, brilliant!
So I consider myself pretty standard and I eventually was able to do it, so I assume there's no special gift necessary for 1 or even a handful of boards at once.
You know I do not know. I would assume you could learn how to do it. You have to work on seeing the board in your head. Then making sure you see how the pieces move. The best way to remember the moves is why the move is being played.
Now playing game blindfolded is not that bad. I have done 6 at the same time with good results but it gets really hard.