You’d need a entirely different class for , instead of static mesh, you’d need to use a Dynamic Mesh, which involves a lot of C++ coding 
I’ll think about it but your request is quite complicated.
Your better off using a dynamic material instance and regulating which parts of the material change to being on fire.
Look up ue4 burn effect / ue3 burn effect to see what people have in the past.
Doing at vertex level just in Blueprints is going to be an uphill battle I surmise.
the key part about a “static” mesh is that it is static, I can’t modify its vertex information at runtime, you need a dynamic mesh for that, which is not yet an official UE4 class.
Check out the C++ Dynamic Mesh thread for more info!