"so" is used in this context to refer back to something previously mentioned. So, in this sentence I would assume there has been some dialogue prior to this statement and this statement is clarifying or adding to that. It may read easier with commas: "Yeah. And, so, what he's doing is he's kicking..." "what" is used as an interrogative (a question word) asking about the nature of his action, that being "kicking his feet..." "What he's doing is..." is really what we would call "fluff". It does not add any new information to the sentence. If left out, the sentence would still have the same meaning: "And, so, he's kicking his feet in the air..."

"So" and "what" aren't being combined here to create "so what" which you might hear colloquially when someone is questioning the reason for something. Starting a sentence with "so" is more of a linguistic habit than a reflection of good grammar. It's commonly used when someone is asking or answering a question, or explaining something, like is the case in your example. Using the word is actually redundant, but languages sometimes have words that allow people to move their lips and make a sound while still formulating what to actually say. In this case "Yeah, and so" all serve this purpose. You'll see people sometimes begin with a long "sooooooo", then sip their coffee just to keep everyone in suspense. This is the best article I could find. I hope it helps. https://www.businessinsider.com/heres-why-everyone-is-starting-sentences-with-the-word-so-2014-5?IR=T