The issue of whether saying "Flame On!" is a requirement for Johnny Storm to become the Human Torch goes to the source of his powers. Storm, along with his sister, her boyfriend, and a pilot, blasted off in a rocket ship of the boyfriend's design. Because of a cosmic storm that the shielding of the ship was unable to block, the four were given massive doses of cosmic rays that changed them into the Fantastic Four.

The fact that their powers were derived from science seems to suggest that there would be no need for clever phrases and secret words for them to activate their powers. But remember this was the golden age of comics and their stories were written by Kirby and Lee. The need for battle cries and such were nearly a requirement. For this reason, the Thing began the use of his famous line "It's Clobberin' Time!" and the Torch began to cry "Flame On!" when he, well, flamed on.

In contrast, heroes like Captain Marvel, Johnny Thunder, and The Demon all have powers based completely on magic and therefore have a mystic phrase or word that must be spoken before their powers are activated.