This passage occurs as a New Testament Lesson in the RCL "Pentecost"/"Ordinary"/"Proper" Season, Year A, most recently October 2020.
Summary: In certain theological circles I often find that justification is the aim; yet for Paul in this passage justification has a purpose. As the Greek indicates, it has a purpose, namely that we would know Christ, his resurrection and his suffering. Rather than claim this is something other than good Lutheran doctrine, Luther and countless other Lutherans have seen justification has the key to the kingdom, but not the kingdom itself, which is Christ.
σαρξ ("flesh" 3:4 and elsewhere) Normally we think that Paul sees the flesh as an entirely evil entity. In this case Paul talks about his righteousness in the law (and therefore the flesh). He never says that his Jewish upbringing was evil. In fact, Paul's whole take on flesh and law provides more a productive evangelical tact than the normal torpedo attack on human sinfulness. Simply acknowledge that people have seen and accomplished great things, yet they still often sense a worthlessness about themselves and are haunted by a sense that something greater exists. To reiterate, Paul is not claiming the flesh is evil, but he is clearly affirming its limits.
ζημια ("loss" or "damage"; found as noun and verb 3:7 and 3:8) Interestingly, Paul calls his accomplishments a loss. The Greek here is a bit stronger in that it can also mean "damage" or "penalty." Paul here lays the groundwork for a later group of Lutheran orthodox thinkers who argued that good works are damaging to salvation. While I don't like admitting this, I can see both Paul's and the orthodox thinker's point here that human achievement can cloud our vision from seeing Christ's blessings.
side note: Paul here echoes back to 2:5 and 2:6 in the Christ hymn; Christ did not regard (ηγεομαι) equality with God as something to be exploited. Here Paul is saying he regards all of his benefits as loss through Christ.
συμμορφιζομενος ("together-shaped", 3:10; noun form in 3:21). I believe this is a crucial word to understanding Paul's letter to the Philippians. Paul writes that Jesus was in the shape (μορφη) as God, but chooses a different shape, one of a slave, for our sake. However, for Paul this does not mean the Christian can avoid death No, Paul believes that we to will be transformed by Christ, in that we will receive the same shape as him -- a crucified slave, so that ultimately, we might receive a resurrected body like his. This is also found in Romans 3:17 - co-inheritors, co-sufferers, co-will be glorified-ers. I would argue that chapter 3 of Paul's letter to the Philippians is applying the Christ him of suffering and glory to the Christian.
διωκω ("pursue"; 3.6, 3.12 and 3.14): Paul's bragging here has a double rhetorical effect -- he will return to the words "pursue" (διωκω) and "righteousness" (δικαιοσυνη) later in this section (3.9, 12 and 14).
σκυβαλα ("crap"; 3:8) Rubbish is about as nice as you can translate this. Paul wants a rhetorical effect here.
καταλαμβανω ("receive, obtain, overcome"; 3:12,13) This verb presents a problem in most cases for the translator because it has a broad array of meanings. In this case, the challenge is in the tenses. In verse 12 Paul claims that he has been obtained (aorist passive) by Christ; yet he also says in the aorist subjunctive that might obtain it; finally, in the perfect active he says he has not obtained it. Here is Paul at his grammatical worst and perhaps theological best: The event of Christ's death and resurrection obtained Paul for Christ, but this process is not finished!
επιλανθανομαι ("forget"; in participle form in 3:13). Most important is not the participle form, but the present tense. Both verbs in the second half (forgetting and looking ahead) in the present tense, suggesting this is an on-going process of doing this. We cannot simply forget once, but must continually forget.
Grammar review & theological commentary on verses 3:9-10
Infinitive purpose clauses In Greek, the infinitive can be used to express purpose, especially when it is an "articular infinitive." (ie, article + infinitive) In verse 9 Paul discusses justification by faith. He begins verse 10 (which the Greek scribes connect with a comma to the previous verse, not a period) with the "articular infinitive": του γνωναι (the knowing). Paul's use of an infinitive here suggests that justification's purpose is to know God, the power of the resurrection and the fellowship of suffering. In other words, 9 and 10 are linguistically linked by Paul and a strong possible reading is purpose...vs 9 (justification) is for the purpose of vs 10 (resurrection). To build on last's weeks passage about μορφη (shape), justification leads to transformation as our "morph" becomes like Christ.