I'm surprised how early it's applied. You can see him covering the hole whilst he's still well into exiting the corner (turn 16). I'm not quite sure how much downforce is actually lost when the flap starts to get blown, but it's probably not as dramatic as I thought if he can apply it so early whilst on the corner like that, I guess.
You don't really need two hands to drive on a straight anyway, It is interesting though as most drivers use their left hands to adjust the brake bias on the straights so it must be somewhere else then for Alonso...
I can't really see from the video his other hand adjusting the brake bias. But he's not going totally hands free, he's still using his left thumb to control the car.
The part of that video I'm talking about is around 1:00 into the video