To flout something is to disregard or ignore it with some degree of brazen ostentation. Flout is used almost exclusively to refer to 'the rules' or 'the laws' in any given context.
Beyond this primary meaning it also has connotations of blatancy, theatricality and general drama-queen carry-on, though I may be spinning this a little through its phonetic similarity to flounce. Which would make a good mnemonic when you are trying to remember the difference between flout and ...
... flaunt. To flaunt something is to show it off, wave it about and generally rub people's noses in it, so in a sense it's the opposite of flout which is to do with the act of ignoring. Again with the connotations of blatancy, theatricality and general drama-queen carry-on, however, which may be where at least some of the confusion arises.
You could, for example, flout the school rules by flaunting the sparkly thong under your little tiny skirt as you flounce about. If you do this, your flouncing will be a way of flaunting the fact that you are flouting the rules.
This is possible but not attractive. I wouldn't recommend it, especially if you are either a teacher or a boy. Or both.