Both flags fallen: Draw? Suppose both players have 0 seconds left on the clock, but the clock indicates that the flag of player B has fallen first, which is claimed by Player A. Player A has enough material to mate his opponent (but also no time left, that is the point!) – has he just won the game?

The rules tell us (emphasisis by me):


  (6.11) If both flags have fallen and it is impossible to establish which flag fell first then:
  
  
  The game shall continue if this occurs in any period of the game except the last period.
  the game is drawn if this occurs in the period of a game in which all remaining moves must be completed.
  


Therefore I think Player A has won. Sadly enough the rules do not explicitly tell what happens if is possible to establish which flag fell first (or at least I was unable to find that paragraph).
If your question is under standard time controls, then player A wins, because it is not the sole responsibility of player A to claim the win; in fact it is the duty of the arbiter to immediately declare the win (so in some sense, it would be unfair not to award player A a win simply because the arbiter was not around when player B's flag fell first), which is the main reason why the clock will indicate which flag fell first.

(If I recall correctly, when Carlsen lost on time against Topalov recently at the Norway 2015 event, it was the arbiter that pointed out the flag fall, without any claim by Topalov.)

On the other hand, in a rapidplay or quicker setting, you need to have at least one second on your own clock to claim a win on time, otherwise either player may claim a draw if both flags have fallen; the arbiter (and certainly any outside observer) will refrain from pointing out a loss on time for either player--even if both flags fall and one player gets mated (or resigns), the win result will stand if neither player notices the other's loss on time.