I see you are deliberately ignoring logic.
Moving fast does not constitute flaming body part. Hardening along with moving fast is how ENOUGH friction happens . It's the same way in which kakakuri was able to launch a fire mochi punch. He first had to use hardening haki. Same with luffys red hawk. Sanji however doesn't need or require the friction needed (the friction needed is speed of the attack combined with armament with a rubber body of sorts or a body of a different composition that's vulcanized with hardening haki).
So it's clear sanjis use of fire is because of lineage factor along with the fact that oda confirmed that spinning is no longer required with sanji having moments of lighting his foot ablaze while being completely still and not moving