I’ve been studying Divine Simplicity recently, and I’m not entirely sure whether or not I ascribe to this doctrine. However, it seems to me that if Divine Simplicity is true, it would be incompatible with a Kenotic view of the incarnation.
In the Stanford Encyclopedia of Philosophy, William Vallicella defines Divine Simplicity as follows:
According to the classical theism of Augustine, Anselm, Aquinas and their adherents, God is radically unlike creatures in that he is devoid of any complexity or composition, whether physical or metaphysical. Besides lacking spatial and temporal parts, God is free of matter-form composition, potency-act composition, and existence-essence composition. There is also no real distinction between God as subject of his attributes and his attributes. God is thus in a sense requiring clarification identical to each of his attributes, which implies that each attribute is identical to every other one. God is omniscient, then, not in virtue of instantiating or exemplifying omniscience — which would imply a real distinction between God and the property of omniscience — but by beingomniscience. And the same holds for each of the divine omni-attributes: God is what he has as Augustine puts it in The City of God, XI, 10. As identical to each of his attributes, God is identical to his nature. And since his nature or essence is identical to his existence, God is identical to his existence. This is the doctrine of divine simplicity (DDS). It is represented not only in classical Christian theology, but also in Jewish, Greek, and Islamic thought. It is to be understood as an affirmation of God’s absolute transcendence of creatures. God is not only radically non-anthropomorphic, but radically non-creaturomorphic, not only in respect of the properties he possesses, but in his manner of possessing them. The simple God, we could say, differs in his very ontology from any and all created beings. 
A Kenotic model of the incarnation can be defined as follows:
According to this view, in becoming incarnate, God the Son voluntarily and temporarily laid aside some of his divine attributes in order to take on a human nature and thus his earthly mission.
If the kenotic view is correct, then (contrary to what theists are normally inclined to think) properties like omnipotence, omniscience, and omnipresence are not essential to divinity: something can remain divine even after putting some or all of those properties aside. 
The Kenoticism derives some inspiration from a New Testament passage: “…though he was in the form of God, did not regard equality with God as something to be exploited, but emptied himself, taking the form of a slave, being born in human likeness. And being found in human form, he humbled himself and became obedient to the point of death…”. (Phillipians 2:6–8, NRSV).
However, if Divine Simplicity is true, and all of God’s attributes are identical to one another and thus identical to God himself, the notion that certain divine properties are ‘give-upable’ is impossible. One cannot ontologically extrapolate God’s e.g. omniscience from his omnipotence. Thus, we would have an a priori reason for rejecting Kenotic Christology.
However, as I said above, I’m not certain whether or not I believe in Divine Simplicity.
(P.S., for what I believe to be a better take on the incarnation, see Timothy Pawl’s article here.)