Does the speed for best glide change with flap?
I presume by "best glide" you mean minimum height loss versus horizontal distance travelled, as opposed to minimum rate of descent?
Assuming you mean the former, then you need to be gliding at the speed which gives you the best Lift/Drag Ratio and, as we know, extension of flaps will decrease the Lift/Drag Ratio and therefore result in a steeper angle of descent.
It's an interesting question and am not sure of the answer!