If you flash and ride the wind back to a bf during opponent's turn do you lose control of the battlefield and score?

Whether or not you score depends on the exact sequence of events, specifically whether you completely lose control of the battlefield before re-establishing it.

According to FAQ #1067 and FAQ #3810, you cannot score if you maintain control of the battlefield throughout the entire showdown. To be eligible to score via a "Conquer" (gaining control of a battlefield you did not control at the start of the current showdown), you must have completely lost control of it first.

Key Rulings

• Maintaining Control: If you use Flash to move your units to base and then Ride the Wind back into the same ongoing showdown, you never technically lost control of the battlefield. Because the showdown does not end until both players pass focus, you are still considered the defender/controller. Therefore, you will not score (FAQ #3810, FAQ #1067).
• Losing and Re-conquering: If your opponent manages to remove all your units or forces you out so that you completely lose control, and the showdown ends (meaning both players have passed focus in a row), you are no longer the controller. If you then play Ride the Wind to move a unit back in, you start a new showdown. If you win this new showdown, you have "conquered" the battlefield and will score a point (assuming you haven't already scored it this turn) (FAQ #9424, FAQ #10791).

Summary of Requirements to Score

1. Lose Control: You must have no units at the battlefield and the opponent must have established control, causing the previous showdown to end.
2. New Showdown: You must move a unit into that battlefield during an open state, which triggers a new showdown.
3. Conquer: You must win this new showdown to establish control, fulfilling the requirement for a "Conquer."

If you attempt these moves during a single, ongoing showdown, you are considered to have maintained control throughout, and you will not be eligible to score.