Hi all, I had the same problem on my S7. Had massive space on internal and external memory, but couldn't save the files from the gear 360 (2016) camera to my phone via bt or wifi. Then I came across another forum, stating that people couldn't save pictures anymore on their Samsung phone with that same message "not enough storage". It seems that the data or cache memory of the "Gallery" app needed to be cleared. Go to Setting, then Apps, then search "Gallery", select Memory, and clear Data. Don't worry, it wont delete photo' or videos. Did that, and the downloading to the phone worked again. Hope this helps for you all.
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