How can I learn to play chess blindfold?
I think you have to take a closer look at mnemotechnics. Probably Memory Palace technique in particular. You can read about it here, for example.

Here is a discussion about techniques used with Chess games. Mainly about memorizing them. A book called How to develop a perfect memory is suggested reading.

If you know Derren Brown (he's British mentalist, a "mind-reader", if you like), he has done a bit about playing 9 simultaneous chess games with top English players. You can watch it on youtube with explanation on how he did it.

Of course, he only had to remember 8 moves at a time, but it's still pretty tricky not to get confused. If you are interested, you can read Derren's book Tricks of the Mind, it has whole section about Memory.

Best of luck!