Clones speak Basic, Mando’a, and a language that is uniquely their own, a combination of basic, mando’a, kaminoan, and random things they pick up around the galaxy, blended together and changed until it’s incomprehensible to non-speakers.
Clone culture is very young, and their language is too. It evolves very rapidly, to the point where the clone language spoken at the beginning of the war would not be understandable to someone who only learned the version spoken at the end of the war. Different units develop their own dialects and slang, and you can tell which unit someone transferred from by how they speak. Certain words, usages, and grammatical features will spread from unit to unit like a meme. Most “popular language trends” like these will fade out of most unit’s dialects fairly quickly, but a few units will incorporate certain features into their dialect permanently. Sometimes the different dialects results in misunderstandings and communication failures, at which point the clones have to resort to basic or mando’a.
Cody, since he’s in charge of the entire Third Systems Army, spends a lot of effort in maintaining fluency in all of the dialects of the units he commands.
Rex and most of the 501st speak 212th fluently, and vice-versa. Cody mocks Rex for his 501st accent all the time, and sometimes Rex will adopt a fake posh 212th accent to needle him back.
There is also a distinct Kamino dialect, spoken mostly by the cadets. This one is more stable than the others, because two of the main factors influencing the instability of the unit dialects- frequent personnel changeover and relative isolation- aren’t present on Kamino. All troopers speak the Kamino dialect, but it’s considered a faux pas to use it in most situations, since it’s a mark of pride and belonging to adopt your unit’s dialect when you receive your first assignment.
Situations where it’s acceptable to use the Kamino dialect are when you are speaking to cadets, or when you are in private and speaking to someone with whom you are very close. Using the Kamino dialect implies an emotional intimacy with someone, and is usually used in private between lovers, batchmates, or very close friends. Conversely, if you speak Kamino to someone you’re NOT close with, it’s considered insulting and condescending, because you’re speaking to them as you would a cadet/child, someone who hasn’t completed their training. You’re implying that they’re stupid, incompetent, unfit to serve, etc.
The clone languages and dialects defy description, partially because the dialects are so diverse and constantly changing, and partially because of spite. One time, a Jedi tried to assemble a dictionary of their unit’s dialect, and the troopers collectively decided that those words no longer meant what they had meant. Conversations were a bit chaotic until new definitions were decided upon. Fun fact, this is why “Jetii”, some variation of which means “Jedi” or “General” in the vast majority of clone dialects, means “latrine” in the dialects of the 94th, 435th, and 104th.