A flame was the visible part of fire. The flame was often the focus of self-balance or religious significance.
Sybo had those in her telepathic circle "[c]oncentrate upon the flame which burns upon the altar of truth," which allowed her to sense the presence of Redjac, whose "[a]nger feeds the flame." (TOS: "Wolf in the Fold")
When Tuvok began to help Kes hone her telepathy skills, he taught her that "[t]he flame of the lamp is fire disciplined, tamed and under control. It is the appropriate focus for the task ahead of us." Tuvok began guiding Kes to attempt to manipulate the flame at the subatomic level, and for her to see the essence of fire, to "[c]oncentrate on the flame. Try to see past the surface, past the light, to the patterns of energy and matter." (VOY: "The Gift")
Later, when he attempted B'Elanna Torres meditation techniques in order to control her anger, he used the same example, stating that "[t]he flame, like emotion, is a primitive force. Left unchecked, it's chaotic, destructive. But if controlled it can be a powerful tool. The lamp controls the flame, as you must learn to control your emotions." This was accomplishedby having Torres "[e]nvision the flame burning within you [...] The flame grows hotter. A point of white light. Follow it backward through the years to a time when you were younger, a child." (VOY: "Juggernaut")
When Dukat prepared to release the Pah-wraiths from the Fire Caves on Bajor, he warned that "[s]oon the Pah wraiths will burn across Bajor, the Celestial Temple, the Alpha Quadrant. Can you picture it? A entire universe set in flames, to burn for all eternity." (DS9: "What You Leave Behind")