His flight is because of the Light Weight Rock Technique. Pretty sure something in DB4 confirms it. That technique is activated to lighten the user, there is no chakra being molded continuously, so he can still fly while invisible. Either that, or there is another explanation, because him becoming visible to use Jinton is proof that he can't mold chakra while invisible.
I'm aware that his flight is an extension of lightened boulder. This scan more or less confirms it
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Onoki was flying when he punched Deidara's clay clone of Kabuto and it was a light punch. Kabuto (speaking through Mu) isn't worried about getting punched by the Raikage since he knew Onoki lightened him, and expected it to be light. Unless Kabuto's interpretation of the jutsu is wrong (unlikely considering he is very knowledgeable about most techniques in general), then flying is an extension of that lightening technique.
I used to think that Muu/Onoki continuously made themselves light and heavy to fly, since if they simply lighten themselves to the point where they are lighter than air, they would just slowly drift upwards and not be able to be extremely agile and move in any direction they choose. Therefore, it's a series of using both light and heavy to move about while airborne. However, this explanation doesn't make sense since Onoki lightened Kurotsuchi and Akatuschi and they were able to move in any direction despite not capable of using Lightened/weighted boulder technique (albeit at a much slower speed than Mu or Onoki.)
There are other possible explanations for Muu not being able to use jinton when invisible, but this one makes the most sense to me.
In short: I'm agreeing with you.