I really don't think this would work. People would end up having conversations in there, anyway, and, even if people didn't, it still wouldn't help much. Have you seen how barren chat has been for the past few months? A trade chat would be even more barren, and, after someone requests a trade, they're bound to leave shortly after, because it's not likely that anybody else will come on and stay in the chat for a while, making it near impossible for two people who want to trade to both be on at the same time without organizing something.
TL;DR: This idea wouldn't work, and if you want to trade with someone, you should probably go to Reddit if you aren't getting any results here.