Flammability (NFPA) - how is it defined?
You have found one of biggest flaws in the  NFPA "Fire Diamond". The NFPA rates the flammability of the compound as a fuel. ClF3 is not a fuel. It is an oxidant. ClF3 is playing the role that oxygen normally does. It causes fuels (reductants) to burn by oxidizing them rapidly and exothermically. Oxidants are incapable of creating fire in absence of fuel regardless of temperature. Fires started by ClF3 continue to burn after being smothered because oxygen isn't necessary to continue the oxidation process. And since ClF3 is denser than air, it gets trapped under the sand. Many other powerful oxidants, like fluorine and perchloric acid, have low flammability ratings. Oxygen also has a flammability rating of zero. They do not burn; they cause other compounds to burn.

The scale for the flammability rating has to do with flash point, which is the temperature at which a fuel forms an ignitable mixture with air. Since ClF3 doesn't burn (isn't a fuel), and doesn't react with air (N2, O2, CO2, Ar, etc, which are all inert towards oxidation), it does not have a measurable flash point. 

The danger posed by ClF3 is summed in the yellow (reactivity or stability) diamond and the white (physical and chemical hazards) diamond. Your msds rates ClF3 as a 3 in reactivity/stability, which is appropriate. Wikipedia's NPFA rating article, even mentions chlorine trifluoride:


  3 -  Capable of detonation or explosive decomposition but requires a strong initiating source, must be heated under confinement before initiation, reacts explosively with water, or will detonate if severely shocked (e.g. ammonium nitrate, chlorine trifluoride).


The white triangle will have appropriate hazard information. For ClF3, it has the symbols OXY, which means it is a strong oxidizer, and W, which means it reacts with water. 

I have not found the specific reaction that ClF3 undergoes with sand (mostly SiO2). I expect that it involves ${\ce{SiO2 -&gt; SiF}}_6^{2-}$, except that this half reaction is not an oxidation.