This may sound like a joke but I’m actually curious, how are time controls handled in Blind and Blindfolded chess tournaments, meaning, how do the players know how much time is left on their/their opponents clocks and how is flagging handled?
If by ‘blindfolded’ you mean a blindfolded simul (like Kolty used to give), then there is no clock, the person giving the simul does the boards in order and when it gets to your board, you have to make your move.
Having served as a second for a blind player several times, the second makes the move on the regular board and then pushes the clock and writes it down.
I think the second can also make flag claims on behalf the blind player (or notify the blind player that his opponent’s flag has fallen and allow the blind player to make the actual claim.)
I’ve never been involved in a time control claim in an event where there was a blind player, though.
For blind players:
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Blind players are allowed a 2nd to tell them info like how much time they or their opponent have used.
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The opponent of a blind player can be a good sort and tell the blind player, when asked to do so, any clock info.
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There are special blind clicks both analog and digital that work for blind and sighted players.
Al Sandrin required neither special equipment nor a second. He would move his own pieces on the board, and had such a good feel for the size of the board that, if the piece was mis-adjusted on its square before the move, it would be mis-adjusted in the exact same direction and by the exact same distance on its new square after the move.
I played him once (he won). Every so often, I’d tell him how much time was left. He never actually asked.
Bill Smythe
It’s actually a legitimate question. The Melody Amber tournaments are half rapid and half blindfold, and I’ve never really thought about how they hand time controls. Anyone know?
In blindfold, though, AFAIK it’s the board position that is “blind,” not the time on clock. (And both piece sets blind or just opponent’s is also a question, to me. One could ‘play blindfold’ but get to see your own pieces IMVHO.)
At Melody Amber, the two players are sitting at separate laptops facing each other. (amberchess2009.com/paginas/photos.html ). There was one photo of Anand-Kramnik that showed enough of the screen to see the onscreen board, and a light colored box in the upper right screen corner. I’d presume that’s the clock.
Maybe you only get to see your own clock? 
But it works for me that clock information isn’t “blind.”
(I know ICC works that way also in Blindfold mode - you can see the clocks quite easily.)
I believe it would be a lot different from full-blindfold chess. I’ve never played the game you propose, but in playing blindfold (esp. multi-blindfold) I probably had almost as much trouble remembering where my pieces were as the opponents’. Once I started to lose a position I would lose my side of it too (but might get it mostly back quickly when the opponent made an unexpected move, like capturing the piece I just gave him for free. That gives a lot of clues 
) And if I saw a board with all my pieces, that would be a lot of help in remembering a lot about the position and the game to that point, so I could figure out where the opponent’s pieces are.
IIRC (though I could be wrong…) I think ICC has both modes available for play. You can play board-is-really-blind and you can’t see any pieces, and you can play where you can see your pieces but not your opponent’s (I think akin to games like Stratego — the actual other position is found blindly.) Though it’s been so long since I’ve been an ICC member I can’t remember.
And logging into ICC as a guest for the first time in forever gave me the answers to my incipient confusion.
There is a ‘blind’ blindfolded style of play. (It is a “board style”.) You get the last couple of moves on the display, get the opponent’s move displayed when made, and make your own moves. But it is ‘blind’ in the sense that there is no “board display” and you have to keep the position in your head. (or Cheaters keep it on a separate board.) And ETA - board moves are typed in via the interface. This can be done with any ICC game IIRC - you can type e2-e4 or just e4 instead of sliding the pieces with mouse.
And, I confused myself with Kriegspiel on ICC, a Wild variant. You see your own pieces, but never the opponent’s - you don’t even know the opponent’s moves. ( en.wikipedia.org/wiki/Kriegspiel_%28chess%29 ) And you ‘feel your way’ through the position by being told what’s a legal move, what’s not, whether you are in check or not, and if I remember correctly whether you have currently checked your opponent.
2nd ETA… In my post earlier about Melody Amber, it looks to my eyes that you can see a board on the laptop screen but there are no pieces on it. (It’s a small photo, though.)