The Flame Fountain is found only in one cave in the western region of Tal Tal Mountain Range. This cave leads to Turtle Rock and first needs to be blown open with Bombs. As Link enters the cave, he will soon encounter the Flame Fountain at the end of a narrow corridor, spewing a constant stream of fire into the passageway. Link cannot get past the flames at all: they will not only cause a huge amount of damage (two and a half hearts worth), but the strength of them will force him back. Not only that, but it cannot be destroyed. Link can only bypass the Flame Fountain if he first obtains the Mirror Shield from the Eagle's Tower in the east. Using the shield, he can force the flames back and pass the trap unharmed.
It is actually possible to bypass the Flame Fountain (and thus skip the Mirror Shield) by taking enough damage from the flames while being in possession of Crazy Tracy's Secret Medicine. Once the medicine kicks in and starts restoring Link's health, he can run through the flames unharmed for a brief period of time.