He gives the explanation in I Cor. 15:44 just a few verses above what you quote. Flesh in his definition, is what we call the body, but his "body" (soma) is made of material derived from the psuche (this is the Greek for "natural", it matches the word nephesh (soul) in Gen. 2:7. The resurrected body is derived from the pneuma (spirit). It can look the same to earthly eyes, but it is different, as is shown by how fast Jesus travelled around after He rose, and how He walked into a locked room, presumably passing through the walls. So, technically, it does not have flesh (sarx), which in Greek, refers more to the edible nature of meat than it does in English.