Pandemic - Can an action be performed by different players during action phase?
No, Flexible Aid Package specifically says that "the current player" takes 1 additional action per card you discard.

So if player 2 uses Flexible Aid Package during player 1's turn, player 2 will discard 1-3 cards from their hand, and that will give player 1 extra actions. Player 2 cannot take the extra actions.

Same with the Borrowed Time event; it only gives the "current player" (the player who is taking their turn" the extra action.