The word "assume" carries with it the connotation of "not really". He did not simply "assume" flesh (as he did in the Theophanies), he became flesh (a permanent condition).
He was and is and evermore shall be "flesh". If he were not "flesh" he could not have died and then be resurrected. Flesh is not something he merely "put on" like a costume, it is something he became.
kostas statement that: "God the Word has no flesh, no form, nor shape, no humanity" connots that "God the word" is not flesh, that G"od the Word" has no shape and He has no humanity," i.e., he has shed his fleshly "costume."
Kosta's statement is in the present tense, which means that as we speak "God the Word has no flesh, no form, nor shape, no humanity." In other words "he is not risen, he has returned to normal."
Do you agree with that?
That might explain why you are balking at it. Historically, it did not carry that connotation; nor does it in my mind. No one is claiming that Christ merely put on flesh "like a costume". He put on flesh via a hypostatic union.
I think kosta's statement, in its original context was referring to the Logos with the human nature abstracted away. Taken out of that context, the statement is obviously false, as kosta would agree. But kosta is trying to avoid another error, that the Logos was eternally enfleshed. So what he means, if I am understanding him correctly, is that apart from the incarnation, the Logos has no flesh, no shape, no humanity. Don't trip up over his use of the present tense verb. He is not intending to speak of the temporal now, but of a timeless truth concerning the divine nature of the Second Person of the Trinity.
-A8