Interaction between Leyline of Anticipation and Teferi, Time Raveler
Leyline of Anticipation won't help you; you will only be able to cast spells on your turn, in your main phases, when the stack is empty.


  307.5. If a spell, ability, or effect states that a player can do something only “any time they could cast a sorcery,” it means only that the player must have priority, it must be during the main phase of their turn, and the stack must be empty. The player doesn’t need to have a sorcery they could cast. Effects that would preclude that player from casting a spell or casting a sorcery don’t affect the player’s capability to perform that action (unless the action is actually casting a spell or casting a sorcery).


So "any time they could cast a sorcery" does not mean literally "is it possible to cast a sorcery under the current game conditions". Instead, it means "could they cast a sorcery under the default rules of the game".

Being able to cast spells as though they had flash doesn't help here, because flash simply means "You may play this card any time you could cast an instant." Due to Teferi's ability, your opponent's turn is not a time that you could cast an instant.

Unlike the rule that defines "any time you could cast a sorcery", there is no similar rule for flash that defines "any time you could cast an instant" as "any time you have priority". So instead, "any time you could cast an instant" is interpreted in the more literal sense; being determined by whether or not the current game state would allow you to cast an instant.

This is confirmed by a ruling on Teferi, Time Raveler:


  If an effect allows opponents to cast spells any time they could cast an instant (for example, if your opponent also controls a Teferi, Time Raveler and activates his +1 loyalty ability), the restriction of Teferi’s first ability takes precedence over that permission.