The word ‘kenosis’, which means ‘an emptying or depletion’, does not appear in the New Testament.
The related verb, ‘kenoo’ is found in Philippians 2:7. There it takes a reflective pronoun ‘heauton’ which is usually translated as ‘emptied himself’.
There are several other usages of the verb kenoo. One interesting one is to ‘empty out or pour away’, and other is to ‘expend’ (Liddell and Scott Greek Lexicon, p. 938b).
Some people think that Jesus emptied himself of something, such as his divinity or his glory. This is not likely. Jesus did not stop being God when he became a man: Jesus, being in the [morphe] form of God (i.e. He still was God when he) … took on the form of a slave, Phil 2:6-7. For example, Jesus showed his divine glory, which he still possessed, to Peter, James and John on a mountain (Luke 9).
Phil 2:7 does not say Jesus emptied himself of something. It just says that He emptied or poured out or expended himself.
How did Jesus pour himself out? By taking the form of a servant, coming as a man and so humbled himself as to die on a cross. On the cross Jesus took responsibility for the sins of all his people so they might go free.
Two other random notes:
Matt 1:21 tells us that Jesus (Yahweh saves) will save his people from their sins. Yahweh-Jesus saves Yahweh-Jesus’ people from their sins. Jesus is God with us (Matt 1:23). Compare Isaiah 43:11( I, even I, am the LORD, and apart from me there is no Saviour.)
Luke 2:11 the shepherds were told that ‘Today, in the City of David, is born to you a Saviour, who is Christ the LORD.’ The Saviour is the LORD (Yaweh) who is born as a man.