The quote in the OP doesn't reflect the actual doctrine of kenosis.
The traditional kenosis view holds that Christ, while fully maintaining His divinity, set aside aspects of that divinity to assume fleshly form.
For instance Christ had to set aside omnipresence since as an incarnated being He could not have causal access to all places at all moments.
Also there are examples of His setting aside omniscience, e.g. knowing the will of the Father concerning the Second Coming, during His earthly ministry.
BTW, I don't fully buy the kenotic theory. As I translate and explain the Greek there I use the example of a glass of water being poured into an empty glass. That is, imho, the word picture used by Paul.
In the history of interpretation on this passage the Church is evenly split.
What would these be examples of, omnipresence?
Nathanael saith unto him, Whence knowest thou me? Jesus answered and said unto him, Before Philip called thee, when thou wast under the fig tree, I saw thee. Jn 1:48
And Jesus knowing their thoughts said, Wherefore think ye evil in your hearts? Mt 9:4
And knowing their thoughts he said unto them, Every kingdom divided against itself is brought to desolation; and every city or house divided against itself shall not stand: Mt 12:25
But he knew their thoughts; and he said to the man that had his hand withered, Rise up, and stand forth in the midst. And he arose and stood forth. Lu 6:8
But when Jesus saw the reasoning of their heart, he took a little child, and set him by his side Lu 9:47