The word is Greek in origin, used by Aristotle to describe "something which can be predicated by other things, but cannot be a predicate of others". To be certain of the correct pronunciation, we would have to consult someone who speaks native ancient Greek, which may be difficult.
The best reference that I could find was this video of a Greek speaker discussing metaphysics.
The gentleman at this link (a male from Netherlands) pronounces it something like HAY-PO-KAAAY-MEN-ON, drawing out the AA sound between hypok and menon.
As a native English speaker, my first instinct is to pronounce it HIGH-PO-KAY-MEN-ON. I would treat the hypo prefix as identical in sound to its use in "hypodermic" or "hypoallergenic". I am less certain about the kei portion, but KAY sounds more correct than KEE. To my eye, the final menon could only be pronounced MEN-ON. Again, this is only my interpretation.