According to Charmander article on Bulbapedia:
A fire burns at the tip of this Pokémon’s slender tail, and has blazed there since Charmander’s birth. The flame can be used as an indication of Charmander's health and mood, burning brightly when the Pokémon is strong, weakly when it is exhausted, wavering when it is happy, and blazing when it is enraged. It is said that Charmander dies if its flame goes out.
Charmander's flame is an indicator to his remaining life force.
So, saying "Charmander dies if its flame goes out" would be like saying "A human dies if he blows his last breath". Dying and having no flame would basically be equivalent statements. So even if Squirtle gets high, squirts all over Charmander's tail and the flame goes out for a second, Charmander wouldn't die and the flame would come out again if he was still healthy.
Having water on his tail will probably cause him a lot of pain and continuously being exposed to this torture could make him faint or die, but it would be because his health would drop and thus the flame would become smaller. Vice-versa, if you could somehow bind a lighter to its tail with infinite gas, Charmander wouldn't become invincible, even though his flame would never die out.