Hmm. An interesting question.
I think they normally can't. In the first episode, Nina, with her Robe activated, fell out of the airship-thing with Arika and Mashiro, and there was no indication that she could fly even alone, much less after catching them. Only Arika's GEM managed to temporarily slow down the fall.
And in episode 3, Arika had to rely on the extensible "straps" at the back of the Robe when holding the airship-thing.
I think it's safe to say that Coral Robes can't fly at least in the "normal" mode of operation. Perhaps there are some kind of limiters that are ignored in the Administar-powered "unrestricted" mode.
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