The answer to how often you can safely flat iron black hair depends a great deal on what condition your hair is in. If your tresses are in any way excessively dry, under-conditioned, damaged or in any other less-than-healthy state, flat ironing won't help, and will likely make things worse. If, on the other hand, you're very good about pampering your mane, you can work out a flat iron schedule for you.
It's generally recommended that heat styling be done no more than once per week. Hair should always be freshly shampooed, conditioned and completely dry before thermal styling. Flat ironing dirty hair will only "cook" soil in and will lead to damage. Even on a once-per-week regimen, heat styling can still be bad for your tresses.
If you're not using an iron with adjustable temperature controls, you need to get one ASAP. Without being able to control how hot your iron is, how do you adjust heat according to your hair's specific needs? Using too-high heat just once a week may still lead to dryness and damage, so make sure you're not applying more heat than necessary. If you hear "sizzling" or smell burning when you touch an iron to your locks, it's way too hot, even once.
Of course, a weekly schedule isn't a necessity, either. To minimize heat damage as much as possible, give your tresses periodic rests from any thermal styling. Instead look into low-manipulation hairdos that allow your hair to fully recover from the effects of heat. You might find a once-monthly flat iron schedule is best for you.
And remember, however much you heat style, regular deep conditioning is a must to prevent dryness.