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.
The KJV, ESV, and NASB all use "flesh" in this verse.