I didn't see your question.
No, it isn't legal in Clark County. They have a vice squad. Although all the standard things like escort services, strip clubs with private rooms, massage parlors, and street walkers exist.
The closest legal brothel to Las Vegas is about an hour drive away in Pahrump. Pahrump has two brothels: Sheri's Ranch, and The Chicken Ranch. They will send a limo for you, you can take a cab, or drive yourself. I lived in Pahrump and worked in Las Vegas. When I was driving to work I was passing a steady stream of limos and cabs going from Las Vegas to Pahrump.
Even in Pahrump, there is nobody in power that is openly "for it". It is just something that is seldom mentioned. But, their taxes pay for the town ambulance service.
Also, I don't know about "Open" prostitution. In the towns I have been in, in Nevada, that have brothels, there arn't a lot of signs and whatnot advertising them. However, the business itself is clearly marked. In Pahrump, they are sort of by themselves at the very end of the road. They are not near other businesses, churches, schools etc. No one is likely to see them, just driving past. They are not hidden, just located off the beaten track. However, they are easy to find, just follow the steady stream of cars. Don't get caught up in the idea that these woman are out walking the streets or working out of their trick's cars. That stuff only exists in places where it is "illegal". However, dispite their laws against it, it exists in every city in the world. Yet another feel good law that doesn't work: just like gun control.