I have created board games and card games, text adventures and scoreboard games with RPG maker... But a chess system? Now that is a challenge. (To be honest... I thought the other systems I made were a challenge too, until I made them. Then I thought them to be easy. Hahaha.)
I have thought about a full on chess system before, but that is like 999 steps further than a simple around the board dice game... Anyhow, how I would go about it with only use of yanfly plugins. (Since I have no knowledge of an existing chess plugin)
I've been thinking about a chess system before, and the best way I could think of, is for each piece-type × each square on the board, you have to pre-program all possible moves. Then, once you have done that (and probably are weeks or even months ahead) you could should add conditions to rule out moves when other pieces are in the way.
That part, that is by far the most work intensive part... By far! It is not hard, but it is a lot of work. Literally 100's of entrees per chess piece. However... You only have to do the bishops once, the rooks once etc. You do not have to do this for each rook on the board, since they all move the same way.
Once you've done that, need to add a bunch of more conditions (again for each piece on the board, this time all 32 of them) to see if they check the opponent king. This is less work, since you've don't most of it already in the previous steps.
When that is done, you basically have yourself a PvP chess game. From here on, making an AI is not that hard, depending on your own chess skills. What you can do is give all different types of move a score (exposing one of your pieces is a lower score, threatening your opponents pieces is a higher score) and then have the AI make the move with the highest score.
It really is not too difficult once you know what to do... It is just so much work. If you start today and work 10 hours a day, you might be done before summer vacation starts.
(I am fully aware there might be simpeler ways, for those who know javascript or any other programming language... But I don't have that. So I would have to take to long way.)
Good luck... And if you happen to find a complete chess plugin after all, even if it is just PvP, then I would just love to hear about it. I wouldn't mind making an awesome chess game.