He feels shame, but it takes a special combination of things for him to feel it. Basically it has to be something he's already self conscious about, like his beaver teeth or his fat ass, and then people need to draw attention to it. For a long time we would never show his teeth, especially in photos, because people were making fun of him being bucktoothed. We were openly mocking him about his weight, so he started lying about losing weight and avoided posting photos where you could see his whole body. He hates that he's white and tries to play it off as being a "white-passing Trans-Latinx".
The things Phil doesn't feel shame about, things that most responsible people WOULD be ashamed of, like being lazy, on welfare, covered in tattoos that look like a special ed class art project, etc., he's actually proud of.
So while Phil does feel shame, it's only over things he feels hurts his self-image and not over things he should feel ashamed of.