Here the metonym "flesh" refers to man in his sinful nature and his achievements. Alternate translation: "about their own human achievements" (See: [[rc://en/ta/man/jit/figs-metonymy]])
Paul uses the word "boast" ironically. See how you translated "boasting" in [2 Corinthians 1:12](../01/12.md). (See: [[rc://en/ta/man/jit/figs-irony]])