L.R.
I'm not sure what you mean by "She tested in for kindergarten" but it sounds like she may have begun too early, before she was really mature enough for first grade; however, you can't undo that now. She seems to lack the maturity to stick with what was a good rewards system for her.
It's late in the school year but don't let this slide. I would have a talk with her teacher(s), in person and not via e-mail, saying you are concerned about this dislike of school, focus on wanting to play, giving up on a reward system that worked, etc., and you would like advice about whether she's mature enough to go on to second grade. Has the teacher or the school said anything about holding her back? Do her overall grades justify that or not? How is she doing overall compared to peers in her grade and class in terms of finishing work -- are they all at her level when it comes to how much they finish, so she's not really as bad a finishing as you think? You need to know these things. Don't let the teacher or school put you off or make it a quick in-the-hallway talk; schedule it, be sure they have a good amount of time to talk, with no interruptions, and ask that all her teachers be there, if she has more than one.
If they suggest repeating (and I'm not saying they will), now is the time. Better to repeat first grade than third or fifth, when the social issues are much tougher. If they say no, she's fine to move on, ask what specifically you can do over the summer to help her work on finishing tasks. You do need to work on this over the summer no matter where she is in the fall. As grades progress, more and more is expected of kids.