What is the concept intended by the numerous times the parsha states that the Jews heard G-d speak from the midst of the flames?
The reason why G-d created the event at Sinai as a voice of words emanating from a fiery mountain is as follows: G-d desired that this event be a proof to all generations that the Torah is of Divine origin - not man made. The one element in which a biological organism cannot live is fire. By G-d creating a voice of "words", meaning intelligence, emanating from the midst of flames, all would know for certain that the cause of such an event was not of an Earthly intelligence. They would ascribe the phenomenon solely to that which controls the elements, that being G-d Himself. Only the One who controls fire, Who formed its properties, can cause voices to exist in fire. As the sounds heard by the people were of intelligent nature, they understood this being to be the intelligent, and metaphysical G-d.
The purpose of the Torah’s repetition was to drive home the concept, which
is supreme and more essential to man's knowledge than all other concepts,
i.e., that G-d gave the Torah, He created and controls the universe, and that
He is metaphysical.
We see the first words heard from the flames were "I am the G-d who took you out of the land of Egypt". This means to say that the Cause of the miracles in Egypt is now claiming responsibility for this event at Sinai. The fact that there were no fires in Egypt shows that fire is not indispensable for the performance of miracles, all claimed by the voice at Sinai. The Jews therefore did not view the fire as G-d, as they experienced miracles prior to this event without witnessing any fires. It is true there was a pillar of fire, which led them by night, but as we do not find fires connected with all miracles, we conclude that fire is not the cause of those miracles, or of revelation at Sinai. There must be something external to fire, which controls the laws of nature, and is above nature. That can only be the Creator.