The Yachtsman is an upscale restaurant. While not V&A, it does have a dress code which is considered business casual. I don't know of too many people who wear flip flops to that kind of venue. I would not. It's also a favorite of a lot of celebrities. We dined next to Mariah Carey a few years ago. I would bring the better shoes. When you make your reservation, you are required to agree to adhere to the dress code before you can get the reservation confirmation number. While it does not mention footwear, I think it suggests discretion.
Dress Code
At this Signature Dining experience, Guests are asked to adhere to the dress code.
Men may wear khakis, slacks, jeans or dress shorts and collared shirts. Sport coats are optional.
Women may wear Capri pants, skirts, dresses, jeans or dress shorts.
Not permitted are tank tops, swimsuits, swimsuit cover-ups, hats for gentlemen, cut-offs, torn clothing and t-shirts with offensive language and/or graphics.