That looks like a lovely dress! I agree with Nicole and Jennifer--seersucker is a weave, but is often, probably mostly, associated as being cotton (in fact, one of my sewing books defines it as cotton in a crinkly weave, another one just defines it as the weave with no mention of fiber). I, too, think it's probably nylon. I generally associate seersucker with being a vertical-pattern weave, but sounds like it can be horizontal as well.
If your listing didn't state the fiber content and the buyer was expecting cotton, I would take the return and issue the refund as long as dress is in "as-sent" condition.
If you don't know how to do a burn test, there is tons of information on the web on how to do one. Even if a burn test is inconclusive, you can "guesstimate" what the fiber is, as long as you say in your listing you "believe this is xxxx...." One of the things that is a sticky wicket for me about buying online is that so many sellers do not list the fiber in their descriptions. Even without a burn test, it's often fairly easy to tell what a particular fiber is because you've handled so much of it. If you have difficulty identifying a fiber and there's no place to snip a piece for a burn test, it could be blend (that's what I sometimes find) and you can often make an educated guess as to what the primary content is. If you don't know what it is, simply state you don't know, and the buyer can then decide to buy, not buy, or ask more questions.
I was browsing a site the other day that sells only high-end items, for several hundreds of dollars (believe me, not to buy anything--just to look!), and a great many of the dresses did not have their fiber content listed. I would never, ever spend that kind of money without seeing, or asking, what the fiber is.....
In any event, the dress is really nice and I'm sure you won't have trouble selling it again!
