Out on the west coast it isn't as common to find tongs at flea markets as I think it might be out east. I did find myself one pair though. They are flat with round groove down the middle. So far I've made 2 pair. One flat, one v-bit. The flat ones are kinda junk, but I abuse them to make them fit pieces, and I won't fill bad if they break The v-bit ones work great (and look half decent), but I made them for some 25mm square bar I have, and I don't do as much forging with that stock. I picked up a pair of Off Center v-bits at the last conference I went to though. They work great! I think I snagged a 1/2" pair. I plan on picking up one or two pair every conference I go to. Grant had a HUGE selection laid out at the last one..
I think the advantage to flat tongs is that they are more versatile in some situations, for oddly shaped pieces, like a large circle you might want to dish into a bowl, etc..