# be found in him

The phrase "be found" is an idiom that emphasizes the idea of "be." Alternate translation: "be truly united with Christ" (See: [[rc://en/ta/man/translate/figs-idiom]])

# not having a righteousness of my own from the law

Paul knows that he cannot become righteous by obeying the law. 

# but that which is through faith in Christ

The word "that" refers to righteousness. Paul knows that he can become righteous only by believing in Christ. Alternate translation: "but having the righteousness that comes by believing in Christ"