A professionally manufactured flamethrower is relatively safe, but grossly expensive. But most homemade flamethrowers tend to be extremely dangerous and fire hazards. Except this one. Though still somewhat dangerous, it's one of the safest DIY flamethrowers you could make.
This video shows the steps to making this Prometheus flamethrower, a one armed flame shooter. It's safer than most flamethrowers because there is no risk of the fire coming back into the flamethrower, if built and used with common sense. Cost hardly anything to make, using all household materials. Try it out.