Psalm 72:9, speaking of the Davidic king, says “May desert tribes bow down before him, and his enemies lick the dust!” It’s not the only time that God/Israel’s enemies are cursed in this way. Isaiah 49:23 and Micah 7:17 both refer to enemies licking dust, and Isaiah 65:25 tells us that “dust shall be the serpent’s food.”
There’s clearly a connection between these texts and God’s cursing the serpent in Genesis 3:14. The question is, what kind of connection exists between these texts? This is really a question about how we go about Bible study. A scholar might search Ancient Near Eastern texts to find that language of licking dust is common ANE language to describe the subjugation of defeated enemies. In that case, both Genesis 3:14 and these later texts would possibly be drawing on older forms. Or perhaps the connection is linguistic, and it would take a Hebrew scholar to dig up some semantic connection involving licking/eating the dust. Maybe the connection is just that licking/eating dust is a universally understood expression of defeat.
But if we read the storyline of the Bible, we can see that God’s enemies are commonly referred to as serpents, and God/Israel’s victory over their enemies is frequently described in terms of head-crushing. Israel’s prophets, during the kingdom and exile periods, draw on the most powerful imagery of God’s promises that they know. The terms, images, and promises snowball throughout history, becoming bigger and bigger.
The Bible was written in a particular historical context within time and space, and that means that to understand it, we need some understanding of the historical context. However, I fear that we may spend so much time going outside of the Bible to historical sources that we miss what the text itself has to say to us. The text itself so often answers our questions on its own terms, if we would only look intently enough to see it.