No, it is not. Most girls wear flats without socks. It is quite common. In fact, frankly, I would say it looks a little weird when a girl does wear socks with flats. As to whether or not it's gross, many types of shoes are worn (and supposed to be worn) without socks, like: flip-flops, heel-strap sandals, high-heels, medium-heels, wedges, canvas shoes, Toms/Bobs shoes, etc. It is totally fine to wear shoes without socks.