Walking represents living, and usually means living according to the true things taught to us by the Lord -- to "walk in His ways." When the Lord is pictured walking, it means life itself.

Flesh has several meanings just in its most obvious form. It can mean all living creatures as when the Lord talks about the flood "destroying all flesh"(Genesis 7:21), or it can mean all of mankind (Genesis 6:3), or it can mean something soft and yielding such as the heart of flesh to replace the stony heart (Ezekiel 11:19) But spiritually it means the loves that dwell in the will of a person, and seem to belong to that person, to be that person. This person may be one who has not started to regenerate (or never will), or one who is in the middle of the process, or one who is near the end. In the highest sense flesh means the loves that are in the Lord's will, which are divine. This meaning is clear in the Lord's words in the gospel of John (John 6:53-56).