When I use FLASH on a ready unit on a battlefield, does it move back ready or does it get exhausted or does it stay in the current state it's in?

When you use Flash to move a ready unit from a battlefield to your base, it stays ready.

According to RiftJudge FAQ #8882 and #6925:

• When a card effect explicitly says to "move" a unit, the unit maintains its current state (Ready or Exhausted) unless the card text specifically states otherwise.
• This is distinct from the "Standard Move" action (Rule 144.2), which requires exhausting the unit as a cost. Since Flash is a spell effect and not a Standard Move, it does not impose an exhaust cost.

Therefore, because the unit was ready at the battlefield, it arrives at your base still in the ready state.