
Maybe both? Maybe he doesn’t have arms in his wings but still uses them to stabilize himself whilst attacking.
Or maybe he stands upright to strike fear in his enemies like some other animals do, but he would most of the time be quadrupedal.
Long live the king...

Well before I read some worrying reports about Milly Bobby Brown's character being able to communicate and possibly control the monsters (Which I will talk about in a separate post) I would have said quadrupedal using it's wings as a front set of legs similar to how most Wyvern's are depicted, but now I am not sure anymore
Look upon my works, you mighty, and despair

He's a wing-walker. #NotMyKingGhidorah

To be fair I don't care if Ghidorah is a wing-walker or not. I think it is the overall design that matters the most. I have seen some fan art of a wing-walker Ghidorah that looks pretty awesome and I wouldn't mind seeing something like that in the movie.
Long live the king...

I'm thinking he'll probably move around quite a bit like that but at certain times will rear up and stand on two legs, looking like the classic King Ghidorah we all know. I'd be totally OK with that. Looking forward to seeing a trailer later today.

Judging by the trailers he'll stand on his back legs for at least part of the movie.
(But if he is quadrupedal then #NotMyKingGhidorah)
“Banana oil.”- George Takei, Gigantis: The Fire Monster

I believe that King Ghidorah will be mostly quadrupedal since the director said he wanted to base him off a dragon. But judging by the trailers he will rear up and stand on his legs to look bigger and intimidate his opponents. Its shown in this photo that King Ghidorah is standing on his wings like a wyvern: Personally I love the change it adds realism to him because it wouldnt make much sense for a dragon to stand on its hind legs for long periods of time, one they’re too heavy and their tails wont give much balance, since wings are their most powerful limbs it makes sense that wyvern like Ghidorah would use his wings for balance, some might say: oh but Godzilla and rodan are gonna be bipedal, well first off Godzilla has a thick tail he uses for balance and Rodan will use his wings for support like a pterosaur would.