flips over

Not flips over, surely, unless it makes a 180° turn, like a somersault?

I would be inclined just to phrase it differently, saying the wiper wipes with the front side of the rubber blade in one direction and the back side in the other direction.

If you had to use a verb, maybe you could say it's angled differently, the angle of the blade changes, something like that?

I suppose it does lean or tilt slightly, but neither of those sounds quite right to me in this context.

And I think swivel might have a more specialized meaning, implying some special high-tech mechanical feature that changes the angle of the blade in a split second, not just what every wiper blade does by its nature. (If I understand you correctly.)

flip over

...was the first thing that sprang to my mind on reading the OP and before reading the other posts.