How do plasma flames work?
In the presence of a strong RF field, ionized air will absorb energy much more effectively than non-ionized air.  If enough energy is absorbed, this will cause some neutral atoms to become ionized.  Meanwhile, some ionized nuclei will reassociate themselves with electrons, giving off energy as radiation (much of it in the form of visible light).  Increasing ion concentrations will increase both the rate at which energy is absorbed and the rate at which is is dissipated.  Up to a certain point, increases in ion concentration will the increase the amount of energy absorbed more than it increases the dissipation, causing a net energy gain (which will in turn increase the ion concentration).  Since only a limited amount of energy is available to be absorbed, however, there's a point beyond which further increases in ion concentration will cause a net energy loss (reducing the ion concentration).

Plasma flames are a cool effect, but I don't know any way to make them safer than real ones (unless confined in something that will keep the RF field in and other objects or fingers out, in which case they'd probably be about as safe as real flames that were similarly confined).  A field which is strong enough to maintain a visible concentration of ionized air is probably not going to be very healthful for any sort of living matter.