“Le” is not a reflexive pronoun. If it were reflexive, it would be either “ándate” or “ándese”.
Over the A. That’s why it’s AN-da-le. “Andar” conjugates to “anda” in the tú form, which carries its accent on the A. You add the -le to the verb (instead of having it float free) because it’s an imperative, and the accent mark over the A to maintain the stress pattern.
It literally translates to “Walk or move” + “third person singular indirect object”. I’ve asked the Mexicans I know and poked around on a forum dedicated to EN-ES questions, and the consensus is that the -le doesn’t refer to any specific third person or object, just that’s it’s a set phrase that means “move it!”
BTW, JKellyMap I’m sure you know this, but for those who don’t:
“Vamos” is correct, but it should be written “vámonos”. You can also use “Vayámonos”, but people will look at you funny.