The first thing to note from the book of Philippians is the fact that the Apostle Paul is addressing believers. Starting at Philippians 2 note the context.
He wants them to make his joy complete at vs2. How? "by being of the same mind, maintaining the same love, united in spirit, intent on one purpose." Vs3, (were still on "how). "Do nothing from selfishness or empty conceit, but with humility of mind let each of you regard one another as more important than himself; vs4, "do not merely look out for your own personal interest, but also for the interest of others."
At vs5, Paul now explains to have the same attitude which was in Jesus Christ, who, although (or in spite of the fact) He existed in the form of God, did not regard equality with God a thing to be grasped. vs7, "but emptied Himself taking the form of a bond-servant, having been found in the likeness of men."
Vs8, And being found in appearance as a man, He humbled Himself by becoming obedient to the point of death, even death on a cross." Vs9, "Therefore God highly exalted Him. Vs10, "that at the name of Jesus that every knee should bow, Vs11, "and every tongue should confess that Jesus Christ is Lord, to the glory of God the Father."
It is my opinion that the Apostle Paul is not specifically writing to prove that Jesus Christ is God, which He is as far as I'm concerned. He's writing to show how Jesus Christ (who is God) gave up everything for mankind by becoming a bond-servant, a person bound in service without wages.
Vs12, "So then my beloved, just as you have always obeyed, not as in my presence only, but now much more in my absence work out your salvation with fear and trembling." Paul is saying to "work out the solution or deliverance of your problems with fear and trembling." Vs13 "for (or because) God who is at work in your, both to will and to work for His good pleasure."
At vs14 Paul is reiterating what he stated at verse's 2 and 3. "Do all things without grumbling or disputing; vs15, that you may prove yourselves to be blameless and innocent, children of God above reproach in the midst of a crooked and perverse generation, among whom you appear as lights in the world."