My opponent plays Elder Dragon and targets my two units at the two battlefields, as well as one of my units in base. If I play Flash in reaction, moving the two units at battlefields to base, will they be dealt damage?

They will not.

Elder Dragon’s play effect has a number of targeting restrictions equal to the number of locations on the board. Its controller chooses up to one enemy unit at each of those locations to target with the ability and each of those units must follow their respective targeting restriction. It is the equivalent to saying “Deal 1 to up to one enemy unit at battlefield A. Deal 1 to up to one enemy unit at battlefield B. Deal 1 to up to one enemy unit in your base. Deal 1 to up to one enemy unit in Opponent A’s Base. …” Each of those targeting restrictions is fulfilled separately for each unit targeted.

If you play Flash in reaction to the play effect of Elder Dragon, any units that are moved to a location other than the one where they were targeted will no longer fulfill the targeting restriction of the Elder Dragon play effect and will be unaffected by the ability as it resolves.