If an ETL said she can change her availability, then a TL has no authority to say she can't. ETL > TL
TL may not like it, but TL can fuck off, as s/he has been overruled.
When it comes to Target, nothing is truly against policy, if someone is willing to approve an exception. When I applied I set my availability on weeknights as 4pm to 10pm, but between when I got hired & went through orientation my husband got a job and his hours were such that I wouldn't be able to go in early to my day job in order to leave early, so I asked to push my availability back an hour on orientation night, and that was approved. We were asked on orientation night for any days off through Christmas, and I had a day job thing that I thought would be on a particular Saturday but I was wrong (it ended up being the Saturday prior to the one I requested off) and I was able to work with our ETL HR to shuffle things to accommodate this without issues. Clearly, availability changes within 90 days aren't strictly forbidden.
It doesn't sound to me like theflowspot ever changed her availability. She applied with availability of 8am. She was hired in softlines under that availability. She was "recruited" by Flow. Flow hours start at 7:30. Whoever recruited her, or their ETL, fucked up in that they did not not set it up in the system so that she could start at 8am, and some people have since been trying to punish her for it.
I can't tell from posts how many TLs and ETLs are involved, but it sounds like nobody is fucking talking to each other at her store, and she shouldn't be punished for that. Maybe she is slow. Maybe they really do need people at 7:30 and the TL/ETL that said she could be late didn't understand the needs of the team and shouldn't have made that exception. Maybe there's a TL on a power trip who doesn't like that she's been granted an exception and is pissed that she's coming in "late" and is trying to punish her for that even though said TL has no real authority to do so (the greatest sin one can commit when dealing with petty tyrants is following the orders of people with more authority than the tyrant).
Shitty leadership happens. It's not always a TM's fault that they're victims of that, and there's no call to immediately assume that the TM is some sort of massive fuckup from their first post.