That’s the problem. I looked in settings and Fortnite didn’t even request permission to use my microphone!
That is not the problem. I’ve tried with both game and party. It just doesn’t work.
So if you go to iPhone phone settings > Fortnite > ... You don't see the following:
Location
I see where you are saying you didn't get the microphone request, but that option should be here but OFF in that case. Let me know and if possible, please post a screenshot of the settings there. We can troubleshoot further after this