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Is there a Christology where "Christ is thought of as divine only, even though he is flesh?" The answer is yes. That is the basic proposition of Monophysitism. The OP speaks of Monophysitism as being exemplified by Doceticism, which denied that Christ possessed a real physical body. However, the historical Monophysite heresy held the view that Christ, though a human being of flesh and blood, had only one nature: divine.
MONOPHYSITISM, meaning "one nature" and referring to the person of Jesus Christ, is the name given to the rift that gradually developed in Eastern Christendom after the Council of Chalcedon in 451. While the definition agreed upon at the council laid down that Christ should be acknowledged "in two natures," human and divine, the properties of each nature retaining their identity, the Monophysites held that after the incarnation the two natures became one, so that all the thoughts and acts of the Savior were those of a single unitary being, God in Christ.
Conclusion: the Christology that proposes that Christ's nature as divine only, even though he is flesh, is Monophysitism.