As it is written in 2 Cor 5:17..."Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new."
Paul served God with his mind, and the NEW skin and bones followed along.
When Paul uses the word "flesh" it is often a descriptor of the previous life style, lived after the fleshly minded lusts.
In Rom 7:25, it is a nod to his past, while he is now living in, and walking after, the Spirit.
I have wished, on more than a few occasions, that he had written "skin and bones" instead of "flesh" sometimes, just to juxtapose the past life from the present life in Christ.
I wish he had used the phrase "fleshly minded" sometimes.
Either way, we can thank God we are now in the Spirit instead of in the "fleshly minded" world.