There are none.
No, I'm serious.
Regardless of design or appearance, if you can hoist it from a flagpole, it is probably a flag. It doesn't have to be rectangular. It doesn't have to have a design. It doesn't have to mean particularly anything.
I make no claim to being a vexillological expert, but I hesitate to acknowledge any set of "rules" for flag design. Certainly, there are certain design tips that for some reason or other, make flags more aesthetically pleasing. The "rule" of tincture is probably the most often cited, and you will often hear me incorrectly interpret it as having a metal (white, yellow) acting as separation between two colors or vice versa. (Corrected, the rule of tincture applies to metals and colors on top of one another, not beside each other, as I apply it.)
Despite this rule, refusing to follow it does not strip your design of "flag" status. There are many flags that violate the rule of tincture, such as Jerusalem, Albania, and a multitude of US state flags. Nobody, I hope, has decided that this rule-breaking makes these flags worse than others, though I might make that claim when it comes to some of the state flags.
As with art, you cannot objectively say that any flag is better than another. Of course, you can like one flag over another, and that is your personal taste, but it is nothing more than that.
But if you must have some tips for flag designing, here are five from the North American Vexillological Association:
1. Keep it simple
2. Use meaningful symbolism
3. Use 2-3 basic colors
4. No lettering or seals
5. Be distinctive or be related
I can confidently say I follow one or two of those. They are things to keep in mind, but if you're designing a flag you shouldn't rule out a design element simply because it goes against one of these principles. Especially given how ambiguous they can be sometimes. How simple is too simple? How distinctive can a flag be without becoming too complicated? I'm not saying the tips are bad; they are quite useful for creating aesthetically pleasing flags. It's just that they aren't rules that you must follow in order to design a nice flag.
I design flags for Touhou characters. Given this, it is often difficult to design flags with only 2-3 colors, or flags that are truly "simple." I try to make flags that clearly represent particular characters, and that have at least a bit of meaningful symbolism behind them. To me, the other principles are of little importance.
There is a reason why the Flags of Touhou do not look like flags you would fly in real-life, and it has to do with the very fantastical nature of the series itself. Their designs are often crowded and complex with little regard for vexillological principle.
But they are flags that mean something!
And that is why I pride over them. Unlike many national flags, they can readily be associated with what they are meant to represent. If someone can name the Touhou character each flag represents without the help of a title, then I've designed my flag correctly, regardless of whatever rules exist for flag design.
I apologize for the rant-like nature of this post, I had a little bout with someone about whether my flags violate vexillological rules. Doesn't matter though, I'll stick with what I do!