I see this is an old thread, but I am going to bump it as I have the same question. I can't figure out how to save a favorite tone (using an iPhone).
EDIT: I just found a post on relating the to FX100 pedal, so the app functionality would apply to the Firehawk. Per that thread:
"I'm surprised to hear that the only way to save a tone to FAVORITES is to search a matching tone for a song in the song library. What if I don't have the song in the song library for which I'm trying to create a tone? Why can't I add the created tone into FAVORITES? This issue needs to be solved as soon as possible. This is a very basic functionality and it is still missing..."
So it was my misunderstanding of the Favorite functionality in that you have to 1st play a song, let the tones load from the cloud, then use the UP arrow to save a favorite. I was considering favorites as a way to mark ANY tone as a favorite for easy recall.