it does not per the both the description of the spell, which says nothing about it catching fire, and per the direct quote of the creator of 5E rules, who also said no, it does not catch fire.
What you do in your home game is on you, what Larian has done by making it catch fire in BG, is just another example of their meddling with the rules, completely changing the utility of the spell.
Again, there is no comparison to burning hands, burning hands requires your wizard to close to within 15 feet to cast the spell, that's the tradeoff, you have to get close to combat. Flammable grease can be cast from 60 feet onto a fire source itself to catch fire or can have a simple candle thrown on it to ignite it, and creates a burning surface that enemies now how to avoid or take damage.
It's utility goes far beyond the simple damage of magic missile.
Again, not arguing that Larian's implementation is balanced. Also not arguing that Jeremy Crawford says grease isn't flammable.
Turning a surface from causing [prone] into causing [Dex ST for 1d6 fire] seems inferior tbh.
