This is a really cool gameplay concept! I had a lot of fun with the chess style battles, and it was challenging without being frustrating. I managed to complete the game in one try, and had a blast doing it!
The audio all worked well. The art style is clean and looks good, though maybe a little more color or flourish to the game-board environment could improve it a bit. I did like the large variety of colorful ally sprites, those looked great!
I did find a UI bug during my game... I guess this comes from my own OCD testing of my games, but I went into QA mode for a second... after each stage, when you get to select a new ally, I suddenly thought to myself, what happens if I try to click more than one while they are sliding off the screen? Turns out I can keep clicking them over and over, getting all options and as many duplicates as I'd like. The character select screen isn't built to hold this many, so they start to go under other UI items and eventually fall off the screen.
Ultimately, this bug didn't break the game, nor did it give me any huge advantage. I basically just used the pieces I would have chosen without any bug exploiting.
Anyway, really nice work! One of the most fun games in the jam that I've played.