Just to check - flyers move :

1) when is their sign on mythos card

2) they move each time monster surge occurs

3) they move each time gate burst occurs

flyer move to sky or if investigator is in neighborhood street then flyer move toward investigator

Flyer lands on investigator. Yes.

Monster surges don't cause any monsters to move.

Flying monsters move:

1. When their symbol comes up
2. When the Mythos card for this turn is a gate burst, whether or not it bursts a gate.

There is no official response for what happens if both occur, but I suspect that flying monsters won't move twice .

Anarin said:

I might be wrong on this, but I think a flyer in Arkham (not in the Sky) only moves towards an investigator on a street if that investigator is adjacent to them. Otherwise they move into the sky even if someone is presently on a street.

Sdrolion said:

no you are not wrong