Flash

Yes, because Flash specifies its destination rather than requiring the player to choose one.

When a spell or ability has the player choose a move destination, that destination must be somewhere other than the unit's current location.^{[355.4][355.4.a]} Flash, however, does not ask the player to choose a destination: the card specifies it as base. That step of the play process never occurs, so this restriction never applies.

The only choice the player makes when playing Flash is which friendly units to target.^[355.5] A unit in base is a friendly unit and meets no other targeting restriction, so it is a valid target.^[355.9.b]

When Flash resolves and instructs the game to move that unit to base, the instruction is impossible — a unit cannot move to its current location. Impossible instructions are ignored, and everything else resolves normally.^[055]

Azir, Ascendant illustrates the same principle: its ability says "Move me to its location and it to my original location," where both destinations are derived from the game state rather than chosen by the player. Choosing a unit at Azir's current location is legal; the impossible swap is ignored at resolution.