I've been looking, and there isn't a Twitter chat for web serials. I'm starting one. It will run on Sunday evenings from 7pm EST until 9pm Est and the hashtag will be #WebFictionChat - if you don't know what a Twitter chat is, it can be hard to explain because it is nebulous.
Essentially everyone mentions that hashtag in every tweet, and we have a two hour conversation. Most chats form around questions, so if you want to suggest possible topics or questions, that would be great.
I'm going to start it from this week, but I expect it to take a while before it builds up any traction. A few weeks or months at least.