Potassium vs sodium bicarbonate in fire fighting
To answer this question, firstly we must understand both how fires are started, and how they are perpetuated. It is common knowledge that in order for fire to exist there must be heat, fuel, and an oxidizing agent (usually oxygen). Once started, a fire is then self perpetuated by a radical chain reaction. Removing any of these three ingredients or interrupting the radical chain reaction can be effective ways of extinguishing a fire. Both sodium and potassium bicarbonate are effective at performing several of these actions, though there are slight differences between them.


Differences between $\ce{NaHCO3}$ and $\ce{KHCO3}$



  It is widely believed that fireextinguishing powders can function as both energy-absorbing materials and solid surfaces on which free radicals can be destroyed. Heat may be absorbed by the heat capacity of the solid [$C_p(\ce{KHCO3})=90.05\:\mathrm{J\:mol^{-1}\:K^{-1}}$ vs. $C_p(\ce{NaHCO3})=87.61\:\mathrm{J\:mol^{-1}\:K^{-1}}$], the heat of fusion, the heat capacity of the liquid, heat of dissociation from breaking of chemical bonds [$\Delta H_\mathrm{decomp}(\ce{KHCO3})=1063.28\:\mathrm{kJ\:mol^{-1}}$ vs. $\Delta H_\mathrm{decomp}(\ce{NaHCO3})=995.72\:\mathrm{kJ\:mol^{-1}}$], and heat of vaporization. All of these contribute to the total endothermicity of the fireextinguishing powder.
  
  From a chemical aspect, it has been found that potassium salts are more effective than sodium salts, and iodide anions are more effective than chloride anions. Presumably, there is a catalytic path for destruction of free radicals, such as $\ce{H}$, $\ce{O}$, and $\ce{OH}$, utilizing the potassium in the salts. It must be remembered that any powder that has a chemical fireextinguishing capability will also have a heat-absorbing (endothermic) capability.$^{[1]}$



The Chain Radical Mechanism



  Combustion of hydrocarbons is thought to be initiated by hydrogen atom abstraction (not proton abstraction) from the fuel to oxygen, to give a hydroperoxide radical ($\ce{HOO}$). This reacts further to give hydroperoxides, which break up to give hydroxyl radicals. There are a great variety of these processes that produce fuel radicals and oxidizing radicals. Oxidizing species include singlet oxygen, hydroxyl, monatomic oxygen, and hydroperoxyl. Such intermediates are short-lived and cannot be isolated.$^{[2]}$



The Chain Radical Breaking Mechanism



  The mechanism by which chemical inhibition occurs when certain powders are added to fuel-air flames is not completely understood. Solid particles may scavenge chain propagating species by surface adsorption or reaction; or alternatively, the solids may vaporize in the combustion zone to produce gaseous products that react with active species via homogeneous gas reactions.
  
  Most investigators seem to favor the latter mechanism, although direct experimental verification is very lacking. If homogeneous gas reactions are, in fact, responsible for the inhibition, then for cases in which potassium salts are the inhibiting agents, the chemical reactions
  
  $$\ce{KOH(g) + H-&gt;K(g) + H2O}\:\:\:\:\:\Delta H = -33.2\:\mathrm{kcal\:mol^{-1}}$$
  $\hspace{78 mm}$and/or
  
  $$\ce{KOH(g) + OH -&gt; KO(g) + H2O}\:\:\:\:\:\Delta H = -1.7\:\mathrm{kcal\:mol^{-1}}^{[3]}$$




[1] Fire Extinguishing Powders

[2] Oxygen Fueled Combustion Reaction Mechanism

[3] Flame Inhibition by Potassium Compounds