What happens when both players are out of time in Blitz? What are the rules when the clock for both players has reached 0?
Are these rules different for digital clocks (where the clock shows who was the first player to flag) and analog clock where it might be unclear who flagged first?

I've had some games in blitz where both myself and my opponent were at 1 second and after my opponent moved, his flag fell and he pushed his clock flagging me as well. When wanting to claim the game my opponent claimed that I should have stopped the clock while I still had time on my clock and since now both of us were flagged the game was a draw. The arbiter agreed with this, but I can't find anything about this situation in the Fide rules.
https://www.fide.com/fide/handbook.html?id=171&amp;view=article

6.11
a. 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.

b. the game is drawn if this occurs in the period of a game in which all remaining moves must be completed.

The only ambiguity is when the claim was made.  If your flag fell after you claimed the win--assuming that you had a possible win--you should have won.  The standard, tactful action is to call the game a draw, but the rules suggest that one should be declared the winner.