No. You can save logs, but that's it. This is a shoestring budget game, so don't expect features like that to ever come.

I would love a program to convert the saved battle logs to a replay video, maybe a short video (cut the time thinking), but you can pause, rew, and ff the video. I think that would be cool.

@fabriono180391 people already answered that question in this thread… there are no in-game replays.

The closest thing to it (this game has) are the game logs that can also be "exported" (basically the button copies Battle Logs to your device's clipboard, then you can paste it into Word or equivalent text file, etc.).