A data point for the benefit of future Googlers:
I was able to do this last week on a Business Flex ticket. I was booked on a 20:50 FRA-TIA flight, but my connection (separate booking) arrived in time for me to switch to the 12:00. I wasn't able to rebook within the app, but it was quick to so in person at the main business check in area outside of Z gates.
I don't know if this is possible for all Flex tickets, but it was for mine.