I have installed, reinstalled, installed from the Galaxy App store the Gear 360 (new) App. It downloads fine. The Gear 360 pairs fine. I hear a shutter sound when I take a picture. The screen on my note8 indicates "capture" when I take a picture. However, everytime I tap Camera on my note8 it just says "loading" for a period of time and then disconnects.
Which Gear 360 do you have?
And I've had a check on the app listing on the Play Store here. Looks like a few people have experienced either the same issue or something similar. Might be worth giving that app's team a shout by email at firstname.lastname@example.org for feedback to them and further assistance (if you've not done so already).
I ended up switching a 16G microchip out with a new 200G chip and the Gear 360 paired and is working fine with the Note8.