If there's Abandoned Hall and they use Flash on their unit, does the unit still get +1 might?

No. The unit will not get the +1 Might from Abandoned Hall.

Here's why: Flash resolves first, moving the unit from Abandoned Hall to your base. Only after Flash finishes resolving does Abandoned Hall's "when a player plays a spell" trigger go on the chain. When that trigger resolves, it asks you to give +1 Might to "a unit you control here" — but your unit is no longer at Abandoned Hall, so it's not a valid target. (This is directly covered by FAQ #11451.)