I'm assuming you start the level at the lower left, next to the green power-up?
You can only "queue up" one power at a time – meaning, that you can grab a power while you are using a power. But that's your limit.
So, the very first thing I do whenever I'm at a puzzle that starts with a green power-up like this is make a point to get 2 uses out of it.
Here is what I think I would do on this level:
1. Hop up through the green, so that I'm ready to use it. (I'll start glowing green, but I won't activate it yet.)
2. Move a little to the left of the green, while I wait for it to restore its power. (It will restore its power before I lose my green glow.)
3. Once the green power-up is restored, I'd jump up and activate green in the air, then fly to the right passing through the new green. (Now I have the green I'm using, plus one more in my back pocket.)
4? I think I'd try to fly straight across to the right and grab that lip that extends under the white power-up, then climb so that i'm standing directly below the white, and I'm still holding one unactivated green.
5. I'd then activate the second green and fly through the white on my way to the upper part of the left wall.
If this method didn't work, I'd have to consider a version where I change to the ball at some point, maybe on the upper right wall. But the first thing I would try would be to do it all with power ups – get a second green while I'm using the first one, and get the white while I'm using the second green.