What is the source of Sanji's flame power?
Well, this is an opinion-based question so no clear answer can be given, but I can at least tell my own opinion.

This was a plausible theory for a time, but in my opinion it is now impossible.

Unless I missed something, nothing indicates that Sanji's Diable Jambe comes from anything other than friction. He's been able to activate Diable Jambe without spinning ever since the beginning of the second part of the series, as shown in the manga by his fight against Surume the kraken; long before his family was even mentioned.

He's been stated several times in the Totto Land arc to be a "dud" whose genetic enhancements failed, a statement greatly strengthened by a revelation from chapter 852.


  Sanji's mother Sora is the reason why his enhancements failed. When she was forced by her husband to subject herself to experiments to allow her then-unborn sons to be genetically altered, she took a drug potent enough to counteract those alterations, in an attempt to cancel them. While this didn't work with Sanji's brothers, it did work with Sanji himself, who turned out as normal and full of empathy and compassion as any normal human.


The above moment's entire meaning and point would be completely shattered if Sanji suddenly turned out to have altered genes after all, hence why I think the theory is impossible. However, this is only my opinion of course, as no clear answer can be given yet.