The writer is going to link up the weakness of the human condition - that's the meaning of the fact that the children all "share in flesh and blood"(14) - that's the frailty we all share - our writer links that with the fact that Jesus "partook of the same things"(14). And those "same things" are the flesh and blood we humans all are born into.
But even here the writer is extremely careful to make a distinction. We frail human beings all "share in flesh and blood" by our natural condition. The Son, in distinction, "partook of the same things"(14). Take special note of that verb, "partook." Here is the mystery of the pre-existent Son taking on a humanity - flesh and blood - at a specific time. You and I don't partake of flesh and blood. Flesh and blood are what we are by nature.