Mixed flock (multiple breeds) or mixed chickens (mutts)?
In the former case, mixed flocks are great. They work very well. Some birds are not suitable for mixing with other birds.
~Chickens with obvious "deformities" such as a single crested Polish in a pen of Barred Rocks, are often not going to do well. The other birds will usually pick, and pick, and pick.
~Chickens that are easily bullied (Faverolles) probably shouldn't be kept in a pen of Production Reds (fairly aggressive birds.)
~If you do get aggressive breeds (and many of the "friendlier" breeds are actually just bolder, ergo, more aggressive) raise them with the more docile ones from the start, and have plenty of space.
But most birds of similar size and shape will do well, and if you have a small flock of a few breeds of very different-looking chickens (so that the flock doesn't have a single victim) it can be an interesting look, and a working flock.
In the latter case, mix whatever you want. Have fun. Post pictures.