It's an expression. Saying someone is a "walking something" means they are a good example/epitome of that thing. Examples: He's a walking encyclopedia of English history = he know a lot about English history. He's a walking dictionary = he has a really good vocabulary. He's a walking disaster area = he is very chaotic - a lot of bad things happen to him. She's a walking fashion show = she wears a lot of very stylish clothes.

In the sentence He is like a walking success story, the word walking is an adjective that describes success story. It means that he is so successful that he seems like a real-life example of success. Yes, the sentence means He is very successful, but it adds a stronger image—it’s as if success itself is walking around in human form. Tip: Words like walking, living, and breathing can be used as adjectives to emphasize that someone fully represents something. • She is a walking dictionary. (She knows a lot of words.) • He is a living legend. (He is very famous and respected.)

Living people walk, and here the phrase indicates that he is a living person. ‘Success stories’ don’t walk. It means that he is a living human example of a success story. Similar examples: I’m living proof that CPR saves lives. He’s a walking encyclopedia when it comes to trees of the region. He’s a walking misinformation machine. He repeats nonsense that he’s seen on social media.

Hello Les. This phrase "...like a walking xxx" is mainly used as a personification of something (usually a concept or object) - In this case, "success story". Another way of saying this is: "If you were to look up the definition of success story ...his picture would be on it"

Yes, his story is going so well