Naruto's chakra does not transfer over dimensions.

[Tera Path]

Well when Minato fist bumped with Naruto and the kyuubi's got in synch everyone that Naruto gave a cloak got more chakra again from the cloak and it became visible again.

Unlike Kakashi, who also got the cloak but is currently in a different dimension.
Many speculated that he did get the cloak but he didn't... which would be a HUGE help because he was
injured and low on chakra.

But now in this chapter we see Kakashi doesn't have a cloak......
Way to go Kishi.......
Oh well, now that that's done.............
So...... hows the weather where you guys are....?

EDIT :

I think this also confirms FTG doesn't work in the Kamui dimension.

Probably.

 

[Touken]

I think this also confirms FTG doesn't work in the Kamui dimension.

 

[Meekz89]

I think this also confirms FTG doesn't work in the Kamui dimension.

Nope not yet

 

[Touken]

Nope not yet

It's the fact that anything chakra wise in the real world is cut off from the Kamui dimension.

Since a Hiraishin seal has chakra in it, I don't think it's possible for FTG users to FTG out of the Kamui dimension and into the real world.

 

[Fuxion]

So far that is nothing but speculation though.