It is made from latex, not plastic.
Latex sheeting is getting glued by rubber cement. Not the easiest to work with depending on your level of experience!
I'm not sure if the surface has been treated with silicone lube, by chemical chlorination process or just left as is.
If going the latex route be prepared for many things to look out for when working with, wearing and proper storage to avoid damage, discoloration and deterioration.
There are shots of coco’s back, aren’t there? That might present a clue about whether his lab coat was modified from preexisting clothing. Eg, his coat may have been a transparent smoke-colored raincoat, which was reversed to act like a smock.