If you’re careful, it could be a good idea. More specifically, if you do this, be careful about which pokémon you choose. Quite a few fighting-types may be too eager or too rough for a human to train with, while some can tone it down (so to speak) to match the limits of their partners.
In particular, starters are very attuned to human partners and thus can adjust their power fairly easily. The downside, of course, is that no “official” starter line is part fighting in their most basic stages, so whichever you choose will need a bit of training before it can begin mastering fighting techniques. That said, of the three (technically four, if one counts chesnaught, although that requires more rigorous training than the others), the torchic line tends to be the most popular due to its flexible fighting style and the fact that it’s neither too fast to keep up with (as in the case of monferno and infernape) or nearly too bulky to train with (as with pignite and emboar). But really, any of them may make excellent choices.
Alternatively, if you can’t obtain a starter, machop tends to be both easy to obtain and easy-going in personality, and as such, it can make for a patient sparring partner. Meditite as well, particularly if you’re looking for a less aggressive approach. Members of the makuhita line are popular among fighters due to their bulk; they can take hits as well as show their human partners how to perform formidable punches of their own. Conversely, hawlucha and members of the riolu line are often sought-after as training partners due to their eagerness to train; it’s fairly easy to learn along with these pokémon as a result.
Whatever you choose, anonymous, always remember that training your pokémon is as important as training yourself. Be sure your pokémon understand your limitations and boundaries before engaging in any sort of training with a fighting-type.
Good luck, anonymous! Your journey sounds like it will be quite interesting, although I admit I don’t entirely know what MMA means exactly. I imagine it’s something like judo?
EDIT: After having discussed this entry with my editor, looked it up, discussed this entry again with my editor, and then discussed it with the lawyer who handles many of the issues surrounding my work, I am now obligated to add that I am not an expert in human sports or health and that neither I nor the editor are liable for whatever happens as a result of my advice concerning either of those particular subjects. I am also obligated to phrase that as “as a result of my advice, however ridiculously terrible it may be” for reasons I’ve been told I’m not allowed to question.