Does flour put fires out efficiently?

Not at all!

Not only because it's combustible, but also because it can cause a type of explosions called "Dust Explosion".

Like the gigantic explosion of flour dust which destroyed a mill in Minnesota on May2nd,1878, killing18 workers at the Washburn A Mill.

And there're actually two types of bombs called "Flour Bombs"!

The best way to deal with a kitchen fire is to gently put a wet towel on the fire; and when the oxygen below the towel is consumed the fire will suffocate.

Any fire needs the above three elements to survive. Putting out a fire is done by eliminating one or more of these elements.

Baking soda is known to act as a reducing agent (minimizing the effect of Oxygen) that's why it might be used to extinguish fires. But since it can be mixed up with flour, it's an unfavorable option.

(And I believe that's how the relation between flour and putting out fire originated!)

Back to the flour explosion; Flour is combustible carbohydates which when dispresed in the air becomes the fuel with all oxygen all over each grain of dust . The smallest spark of heat can trigger the explosion as showen in this video.