If you have an upcoming move this is a valid question. Some moving companies will either do one or the other. In most instances if it’s a reputable Las Vegas moving company your rate will be hourly. I don’t see how you could receive a flat rate for moving in Las Vegas based on your items.
Now what you can do is have a Las Vegas mover come out to your home and give you an in-home estimate. The estimator will conduct a survey of your home and then provide you with a not to exceed moving quote. This is somewhat of a flat rate, but not the type that your amateur moving company provides. Research your movers. Don’t go for those that ask for a list of your items. Choose a quality Las Vegas mover that will handle your items and time with maximum care.