In Pandemic, can an action be performed by different players during action phase, by using Funded Event cards? For example: "Flexible Aid Package" allows a. player to perform 1-3 extra actions (by discarding cards). Can this card be used by "player #2" while "player #1" is in the "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.