Stingray classic 5 with flats?

I’ve got an awesome classic Ray 5 in Lake Tahoe blue. I also have a Sterling 5H. Both are strung with regular Slinkys. I’m thinking of stringing the Ray with flats. I have a P bass strung with chromes, and I dig the tone. Do you think I can get a similar tone, and if so, what brands of flats have a decent B string?