Because you indicate that you're from New Mexico, I'm assuming that you're asking about the rules governing curbside mailboxes used by the United States Postal Service.
If that's the case, there are constraints on the design of signal flags, but they are far more focused on function and ergonomics than on aesthetics, and they can be found at USPS STD 7C, which says:
The flag must be mounted on the right side when facing the mailbox from the front. The flag must not require a lift of more than 2 pounds of force to retract. Additionally, when actuated (signaling outgoing mail), the flag must remain in position until retracted by the carrier. The color of the flag must be in accordance with the requirements described in 3.9. The operating mechanism of the flag must not require lubrication and must continue to operate properly and positively (without binding or excessive free play) after being subjected to the test described in Section 4. Optionally, the flag may incorporate a self-lowering feature that causes it to automatically retract when the carrier service door is opened provided no additional effort is required of the carrier. The self-lowering feature cannot present protrusions or attachments and must not interfere with delivery operations in any manner or present hazardous features as specified in 3.1.
The regulations provide "preferred" designs -- generally the rectangle you're likely used to -- but say that other designs may be permitted if they meet the other requirements.
As I read it, this means USPS doesn't care if you use a circle or a square or a triangle or a swallowtail, as long as at isn't too heavy to lift, too flimsy to stand up on its own, etc.
