Both have almost too much in common,
- Both are Fighting types i.e they have similar coverage and similar weaknesses. Of course I said similar which doesn't mean exactly the same, but there's no fun in "similar" either.
- Both are horribly frail most of the time.
- Both are physically oriented, which limits the coverage they can have.
Blaziken and Breloom both have one common goal as physical fighting types: hit hard, and hit fast. For Blaziken with it's speed and ability, and for Breloom with priority Mach Punch. They both do the same thing, and it's redundant to have that going. That slot could have been much better utilized. They even share a common Flying weakness, attracting Talonflames from across the globe.
People sometimes do run bulky SubSeed Breloom though (personally I still think that's too frail), and it might have some better use with Blaziken.
If you really want to use them together, then you should have good reasons to, otherwise it's rather pointless. There's always a better option most of the time.
However, if this is in-game, anything works. It wouldn't matter how unviable your team might sound in it, people have done it with Grumpigs and Luvdiscs before. Blaziken and Breloom are no exception.
Hope I helped!