engaged in the same conflict that you saw I had and now hear that I still have. (Philippians 1:30, ESV)This completes the sentence from verse 29 and it also completes chapter 1 of Philippians.
The conflict is not a physical fight with opponents, "... for we wrestle not against flesh and blood..." (Ephesians 6:12) Paul in engaged in a conflict against the Spiritual Powers of this world. He is fighting to continue spreading the gospel. The powers that be are aligned against him to stop the spread of the truth. Paul is tying up this section by going full circle. He began, thankful for their united effort to spread the Gospel. Now he is encouraging them to keep that battle going. Paul and these Philippian Christians are in it together.