Of those (even ignoring the duplicate with in A), the best option is B.
For example, according to Duke University:
Instructors should not grant students permission to leave class early or arrive late when their class conflicts with another on the student’s schedule.
Option A (after removing the extra with) isn't natural because it makes it sound like the classes are literally fighting each other.
Option C is a little bit harder to analyze beyond people don't say this. Still, I think the problem with it is that it's just not forceful enough. For example, note how the coinciding is a good thing in the following church announcement:
Childcare is available during this time, since the class coincides with our regular Wednesday evening activities.
Of course these aren't the only options, happens at the same time as and similar are also acceptable:
How do I take two college courses that are scheduled at the same time? — Quora
Also, I (being American) would understand "clash" in this context but wouldn't be likely to use it, so characterizing it as non-American English seems accurate (it seems to be used in Australian English in addition to British).