Okay, this has a lot of dispute across forums, and it's something that I have been trying to confirm myself. As far as I can personally tell, it does not boost Acrobatics, even with Flying Gem. The Gem is consumed before the move is used, so Acrobatics gets a x3 boost. However, the Technician ability seems to activate after the Gem is consumed (i.e. after the held item is checked), and since the base power is now above 60, it will not boost Acrobatics. Same with after the Gem is consumed; held item is checked first, then Ability is applied. With no held item, Acrobatics is at 110, so no Technician Boost.
The only instance Technician will boost Acrobatics is if the Pokemon using it is holding an item that is not a flying gem; then, its base power will be 55. 55 x 1.5 = 82.5, so it's less than Acrobatics w/ no held item (110).
It also seems to be a different case than with items like Choice Band; the band boosts Scizor's moves along with Technician. Acrobatics - as a move - checks the held item before it's executed, specifically because its base power depends on the item the Pokemon is holding, unlike other moves like Bug Bite, Bullet Punch etc. that don't rely on a held item.
Discussions of Technician Acrobatics:
Link - last post here has someone testing it out in-game.