Depends on the type of CoC, but generally it either can't be done or isn't worth it.
First of all I am assuming you are talking about pretty much 100% RF uptime, not just turning it on for bosses and stuff.
For CI fakener (the strongest currently existing CoC build), absolutely not under any circumstances. CI fakener builds already struggle with getting enough base ES because they require a Voll's Protector, and they end up getting most of their base ES from their shield as a result. Going RF would require you to replace your shield with a Rise of the Phoenix, which would leave you with extremely low ES.
With that out of the way, let's look at what it takes to properly sustain RF:
With a level 20 purity of fire and a rise of the phoenix, you will have 87% max fire res. Righteous fire burns for 90% of your life as fire damage per second. So, with 87% fire res, you will need to regenerate at least 11.7% of your life per second to sustain RF. Getting 11.7% life regen on a build that generally wants to be mainly in the upper right corner of the skill tree is extremely difficult - In the entire upper right quandrant of the tree, there is a grand total of 2% life regeneration.
While it's possible to get SOME amount of life regen, or additional max fire res, from outside of the passive tree, you generally need to get the large majority of it from your tree. In order to do this you would need to go massively out of your way to the templar/maurader/duelist area of the tree, and the amount of damage you'd be losing from missing countless spell and crit nodes would be greater than the amount of damage you'd be gaining from RF.
And on top of all this, if you are going RF you can't take Vaal Pact, which means you lose MASSIVE amounts of survivability, and you will also have extreme difficulty dealing with elemental reflect.
It is technically possible to use RF without having enough life regen by constantly leeching and keeping ruby flasks up, but even then you are still going to be losing out on a lot of survivability.
So overall, while it can sometimes be sort of possible to sustain RF on a CoC build, it's almost always not worth it.