What do you better luck with against a Gleaming Blissey - Flareon or Machamp?

Machamp. Just dodge. That's with Zen Headbutt added to the picture as well.

Probably comes down to what you have available. I have a maxed perfect Machamp and i do fine since Dynamic Punch generally allows me to dodge the gleams, but I just got ahold of a couple of good Flareons so I might give those a whirl (I don't see myself liking them more though).

Those lucky enough to be blessed with a Focus Blast Mewtwo (like my casual friend) needn't worry about Gleam hardly at all. If you have legendaries available, an Entei or Moltres might serve you better (I'm maxing out my Moltres soon and I think it'll give Gleam Blisseys a run for their eggs)

Moltres, Flareon sucks.

Machamp ftw, given that potions are well in excess anyway.

Only use Flareon (or entei Moltres) if you need to Netflix and battle or something so you can ignore dodging

Machamp. Always.
It can lower the motivation of a ZH/DG to 0 without potions. A bit of dodging is required for this. You don't like dodging? No problem, just don't do it and finally get an use for all those revives and potions flooding your inventory

Flareon.
If the CP is more than 3k, I use Machamp first till it faints, then Flareon to finish it off.