An FAA policy statement we use constantly to show compliance to 25.853 is PS-ANM-25.853-01-R2 (the R2 is the revision level) as it has a number of FAA approved means of compliance. I am not an FAA DER/ODA UM for flam so I cannot speak with authority, though I write a LOT of flammability test plans that have to be approved by an FAA DER/ODA UM for flam.
Regarding the new finish meeting 25.853, the issue we typically run into is when a manufacturer specifies their material meets 25.853 they usually have their own internal testing but very rarely have "FAA-witnessed" flam testing. "FAA-witnessed" means an FAA DER/ODA UM for flam witnessed the accomplishment of an approved test plan with conformed coupons and then signed to find compliance for the test results. Even if they have FAA-witnessed testing on file, we then have to consult PS-ANM-25.853-01-R2 to see if the substrate the manufacturer used for test can be an acceptable means of compliance for whatever substrate will carry the finish on the aircraft. That determination belongs to the FAA DER/ODA UM for flam assigned to your program.
The issue as I understand it from my non-FAA-delegate perspective is that the finish and the substrate can interact in unpredictable ways for flam when combined, and thus the FAA is cautious concerning similarity statements. There are some finish/substrate combinations that suppress flam propagation and there are some finish/substrate combinations that accelerate flam propagation. Without testing, or alternatively showing an already accepted Method of Compliance for the combination via the PS-ANM-25.853-10-R2, it is an unknown that must be resolved.