I had this problem because I had previously accepted an internal test-flight code from my work email on me personal Apple ID. This seems to bind your personal account to the internal testing for that app and you can't accept the internal testing from your work account.
Unfortunately it can take up to 90 days to undo this:
In AppStore Connect go to Apps > Your App > TestFlight > Testers, All.
Find your account in this list, select it, then press Delete
Your status will change to "Deleted: Build expires in X days".
You now have to wait X days (yup) for all builds you had access to to expire.
Check that your name no longer appears in the list of testers, once this has happened the binding has been undone and you can re-add yourself to internal testing and get a new redeem code.
Topic:
App Store Distribution & Marketing
SubTopic:
TestFlight
Tags: