[quote=@Lugubrious]
<Snipped quote by ModeGone>

I think I've gotten the picture, although it's still a little confusing. I do think that simply being able to make himself two-dimensional would be a very useful Power in and of itself, without any extra confusion. Is able to become just a line in his game?
[/quote]

Kiiiiiind of?  The thing about him becoming a line in the game is because when you see yourself use the Flip within a dimension you are turning your character sideways.  Because they're a flat character and the rim of the paper-figure is facing the screen, they become "invisible".  In the Paper Mario series you had all kinds of weird shenanigans playing on the "paper" theme like getting folded up into a paper airplane to fly across long distances or walking through iron bars because you're paper-thin.  Changing dimensional perspective is following that kind of effect but with a result.

However like I said this is a 3D person.  Trying to rework this effect without being a simple rotation implies that there's an actual effect.  Since its not an Illusion and doesn't have anything to do with light I can't say that he looks invisible until you put your hand where really is and you feel him.  So I'm overthinking this...

The two main effects that Flip has:
[list][*]Letting you walk around objects (be they enemy, prop, or attack) by going down the other axis.
[*]Travel to another world/dimension.[/list]
With the first form it is technically turning invisible and has been used to this effect by various characters.  But you're still physically there so things like weight remains the same and since you only see the characters in the game from the side/front perspective I like to think that top-down would be a whole other story.  Given the setup and how the effect has an actual upgradable timer in game, I'm going to say it'll last two or three posts in the current form.  I also like the idea that light casting shadow on the "invisible" character would let you see the shadow as if the figure was standing there normally as it would give more of a challenge to sneaking around.
With the second I have it completely blocked until necessary because we're on one world and the character would take the opportunity to ditch given half a chance.

So in theory he could just be turning into a line because going from 3D to 2D would have a weird visual effect.  Or following the displayed effect in the game he'd be "turning into a line" because of the way dimensional perspective is warping around him.  In the end its the same kind of result but it has different connotations in my head that I'm having a tricky time spitting out.