Not sure I understand this correctly. If I am an active player, I can play as many sorceries including cards in my graveyeard with flashback before I pass priority for the other player to eg. counter?
No, because you can only play a sorcery when three conditions are met:
1.) The stack is empty.
2.) You are the active player.
3.) It is your main phase.
If these three conditions are not met, then you cannot play a sorcery. This is why, if you want to flashback the Deep Analysis, you would have to play it immediately from your graveyard after it resolved. Otherwise, if you pass priority, then your opponent could use an ability to remove it and you couldn't respond by flashing back the Deep Analysis (as the stack is not empty at this point).