Gym speakers plus your own music plus clanging plates makes messy audio. For voiceovers, record them separately.
Fitness / Recording workout videos with your music playing
Guide
Recording workout videos with your music playing
Short answerUse a camera app that keeps other audio playing, and remember music in headphones won't be in the video. If you post, you need the rights to the music.
About Music Wide Selfie
An iPhone camera app in development for people who film themselves. Not released yet; one email when it is.
One email when the app is ready. Nothing else.