Bottom line, the rules don't say that there's a "chance" of flammable objects catching fire. It says they catch fire, period. There isn't a Save, a resistance check, a test to see if the spell did a minimum amount of damage or met some other special threshold standard. The spell does what the rules say it does.
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In a game mechanics discussion there is no doubt, no room for error. The spell says it lights the thing, so it lights the thing.
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All that's left is to determine how much damage being on fire does, and how many hit/break/structure/whatever points a heavy wooden door has.
Since the rules don't state how long the fire lasts or how much damage is caused by the ensuing fire, that part is left up to the DM.
I would rule that the door smolders for a moment, then goes out. Being lit on fire did 0 damage.
In addition, charred wood is not particularly flammable (I included a reference in my first post). Heck, steel is flammable under the right circumstances. But even ignoring that, I would rule that the best the spell could do would be to burn a fist sized hole in the door. Eventually you may burn down the door but it will take a long time. All while following the rules or lack therein.
Just like eventually you could probably break down a door with arrows.
But this really goes back to what type of game you want to play. I'm not a slave to the letter of the rules and sometimes common sense takes precedence. To each his own.