I wrote it above and will write it again. The Greek text in Rom. 8:12 very clearly uses the word "sarks" which is the flesh. Paul never uses "sarkos" when he means old man or sin nature. They are two very different things.
The KJV, ESV, and NASB all use "flesh" in this verse.
Paul uses the term flesh interchangeably to refer to both the body and the old man depending upon the context.