It might help us make suggestions if you stated what phone model you have and which version of Android its running.
In the meantime, not knowing if this is a hardware or software issue it's not going to be easy to find a definitive solution. If you have have a flashlight app or some other app that utilizes the flash LED, have you tested it using that to see if the LED is working? If it is working at least that eliminates a hardware problem. If the flashlight app doesn't work either, that's an indication the LED could have failed. Replacing it generally requires disassembling the phone, with some skilled soldering involved to replace the actual failed component, so unless you have all the necessary tools and are comfortable doing such things, or know someone who is, it's better to have something like this done by a trained technician.
But if the flashlight app does work OK, there's probably just some issue with the camera app. Try doing into the Settings >> Apps menu of your phone, find the Camera app entry, open it and tap on the 'Force stop' button, then find the 'Clear data' button and tap on that. This clears any settings in the Camera app, essentially returning the app back to its original, first-time used state, and it clears the app's cache.
Now try to start up the Camera app again and see if that made any difference.
If the Camera app still has problems with the flash, you could try installing a third-party camera app from the Play Store. There are a number to choose from but I'll just recommend the 'Open Camera' app:
https://play.google.com/store/apps/details?id=net.sourceforge.opencamera&hl=en_US
It's an Open Source app, free with no ads, and has a really good feature set, probably more than the default camera app in your phone. Anyway, try a different camera app and if that also has problems using the LED flash there's something else going on, more likely at the operating system level. But again, it helps to know what phone and which version of Android you're using.