HOWEVER, I deeply regretted it and did it in a different order on my Hero Mode run (and intend to do it this way every time I play it from now on). The order that I feel is objectively the best is Power, Wisdom, and Courage. It's clear that Power is the easiest to get, so I think it's obvious that they intended something of a reverse order compared to finding the flames.
To take that a bit further, note that the Sky Keep actually does have a boss and miniboss. The miniboss is Dreadfuse, and instead of a traditional dungeon boss you have the miniboss gauntlet fought in the Courage-piece room. I think that you were sort of intended to do this last because it's the boss of the dungeon, and even if you weren't, I think fighting the boss gauntlet last is just funner. So although you can often get Courage before Wisdom, I always do Courage last because the miniboss gauntlet is an awesome finale to the Sky Keep.
Hopefully now you've all seen the error of your ways.
Power, Wisdom, Courage is the order that I did them in. I'm not really sure if I had any sort of plan to do it a specific way, but that's how it came out. For some reason it just seems kind of right for Courage to be last, in my opinion. That order seemed to work pretty good for me, and I don't intend to do it a different way next time, I just hope I remember everything I did since I was able to go through it pretty fast the first time. :>
I got them in this order: Power, Courage, Wisdom. I was trying to get courage first, but I found myself in the power place instead. So I went ahead and got that, found out how to get to courage, then got that too. Wisdom was hard to get to, but I stumbled on it eventually.