The problem with so much of skepticism is that it is self-refuting. Flaubert's aphorism is an example. If he really means that we should believe in nothing then he has to admit that he doesn't believe that we should believe in nothing. This, of course, is incoherent.
Flaubert wants to make an exception to his skepticism for Science, but in order to believe in Science he has to believe in a host of other things as well. He has to believe, for example, that Reason leads to truth, he has to believe in the trustworthiness of his senses, he has to believe in the orderliness and uniformity of nature, the reality of an external world, and so on. In order to place his faith in science he must set his skepticism aside, otherwise it's sure to get in the way.
Despite his silly assertion about throwing out all one's beliefs, Flaubert didn't really mean that we should literally believe in nothing. I don't think he was a complete nihilist. But it would be interesting to know what sorts of things he thought unworthy of belief and what his reasons were for not believing in them. Maybe a reader can enlighten us on the matter.