I just worked through this myself. You have a couple options. You may need to use a tool like Handbrake to convert your file to MP4 (even if it's already MP4). Otherwise your audio will be out of sync. Alternately, I JUST found out about OBS Studio somehow. In that case, you can change your output settings to MOV which should import to Resolve with no problem. Although, I've not had a problem importing MP4's from OBS Studio yet, I had a lot of issues doing so with OBS Classic. Everything I've read seems to point to using MOV for some reason.
Now, what I can't figure out is how to import multiple audio tracks (one for system and one for mic) so they can be edited separately. The tutorials I've found online don't seem to work for Resolve. It always shows only 1 audio track.