One of the odder characters in the DCU, Plastic Man does have a history with Batman, especially in the Batman The Brave and the Bold comics and TV show.
For there, he was a criminal, who suffered an accident after being foiled by Batman. Batman took pity on him, and helped him become Plastic Man, but Plastic Man's criminal past kept coming back to haunt him, making him lose focus on what was important.
However, eventually, he straightened out, and become a powerful ally for Batman. Albeit, one that Batman wouldn't mind not having around most of the time.