He was born in human likeness, appeared in the shape of humans, but because of his powers he was at the same time in the "form of God". That is, the earthly Jesus had that thing which Adam wanted to grab from the tree, even though it was forbidden, that thing which the snake promised to him: to be like God.
But even though Jesus was "equal to God", "in the form of God", as he wandered about in Palestine, he willingly disregarded (the 'kenosis') his divine authority, i.e. "he humbled himself", and let himself be killed for the salvation of others. He was in "the form of God", but "he took on the form of a slave", i.e. a slave for his fellow humans, thus "not looking out for himself but for others".
So, the laudible attitude of Christ which the Philippians must emulate, according to Paul, i.e. "each one not looking out for yourselves but for the others", was not the decision Christ made when he was in heaven to give up his heavenly existence and become incarnate so as to be executed. It was the decision he made when he was in human form.
Each one must look out not for yourself but for others.
Think that within yourselves, which was also within Christ Jesus,
stanza 1
who being in the form of God did not regard being equal to God as a grab,
but made himself of no effect, taking on the form of a slave.
stanza 2
Having been born in human likeness and appearing in the shape of a human
he humbled himself having become obedient to the point of death, and death on a cross.
stanza 3
Therefore God also highly exalted him ...
(Phil 2:3-9)
That he "takes on the form of a slave", then, does not refer to the incarnation, becoming human. It means how he acts as a human. That he "takes on the form of a slave" refers to the exact same thing as "becoming obedient" in stanza 2. In this way it is not a three stage progression from heavenly existence to incarnation to the cross. Instead there are two stanzas which form a parallellism, both describing Jesus as a human.
The first stanza describes Jesus' going to the cross within the perspective of his divinity, the second stanza describes the same thing within the perspective of his humanity.
Kenosis
The term "κενοω" used in stanza 1 I have translated as "made himself of no effect". It's first meaning is "to empty", but Paul himself also uses it several other places. All these places he uses it in its extended, abstract meaning. In 1 Cor 9:15 he is proud because he has not made use of his right to material support from the Corinthians, and "no one is going to empty" this boasting of his, meaning in some way to remove from his boasting that which makes it boasting.
In 2 Cor 9:3 he again uses it in connection with his "boasting". Paul is so very proud of his Corinthians, because they are so willing to give money to the community in Jerusalem, and he boasts about them. And he says that he is sending a collector now, so they can give the money, "so that with regards to this my boasting about you won't be emptied". Again, the idea of "emtpying" is the process when the thing becomes devoid of that which defines it.
In Rom 4,14 he says that it is through faith, not the Law, that one becomes an heir to the promise to Abraham, and therefore if it was instead through the Law, then "faith has been emptied". Meaning that faith has lost that which makes it faith.
In 1 Cor 1,17 he speaks to the Corinthians about his gospel preaching which is "not in words of wisdom, so that the cross of Christ will not be emptied". He also reminds them of his first preaching to them which, likewise, was "not with persuasive words of wisdom but with a demonstration of spirit and power" (2:4). So perhaps what he means with "the cross of Christ" being "emptied" is that if the preaching about the crucifed Jesus is not accompanied by miraculous deeds (or "a demonstration of spirit and power") it fails to make people come to faith. The "cross of Christ" is then devoid of the special power it effects on the mind.
So what does it mean in Phil 2:7 with "κενοω" when Jesus "being in the form of God ... emptied himself taking on the form of a slave"? Obviously, it means that he makes himself so that he is not in "the form of God", but in what way? It can perfectly mean that he incarnates, but then "the form of a slave" must simply be another way of saying "the form of a human", and that is kind of a strange choice, I think.
To me, the term is abstract enough that it might also well be used to describe the way Jesus chooses to give up or disregard his divine authority as he lets himself be handed over to crucifixion.
The idea I'm thinking of is expressed well in Matt 26:53, when Jesus willingly hands himself over to crucifixion in Gethsemane, even though he has the divine authority to "send twelve legions of angels" to his aid. Is this the way Jesus "empties" himself of his "form of God" and "takes on the form of a slave"?
Then Jesus said to him, “Put your sword back into its place; for all who take the sword will perish by the sword.
Do you think that I cannot appeal to my Father, and he will at once send me more than twelve legions of angels?
But how then would the scriptures be fulfilled, which say it must happen in this way?”
(Matt 26:51-54)
Here Jesus "makes himself of no effect, being in the form of God taking on the form of a slave ... becoming obedient to the point of death". In a way, then, this emptying element is the exact opposite - perhaps even undoing - of Adam's transgression, as he grabbed being equal to God. Adam grabbed the fruit to become equal to God, Jesus 'emptied' himself from being equal to God not regarding it as something to be grabbed.
If the emptying thing and taking on the form of a slave thing does not refer to the incarnation, as with this reading, then it doesn't change that much in the context of the letter, of course, Paul's message to the Philippians remains the same. But it removes the idea of the incarnation from the hymn. One could also say that in this way it makes Jesus' mindset even more relatable to the Philippians, as Paul is only speaking about Jesus' actions as a human.
He was in human form like the Philippians, and he willingly died for the sake of others, even though he had divine authority. So much greater was his neighborly love to emulate. I mean, it's quite laudable that he would choose to give up his divine existence in the heavens and be incarnated as a "slave", but this aspect of Jesus' self-sacrifice is just not that relatable as an example for the Philippians to follow.
When Paul exhorts the Philippians, could this not be described as "taking on the form of a slave"?
Each one must look out not for yourself but for others.