What is a #"facile chemical reaction"#?
A facile reaction is one that is easy and simple to do.
Check this definition. A facile chemical reaction could be the formation of an acyl halide by treatment of a carboxylic acid with thionyl chloride, or the formation of an ester by thermolysis of an acid with an alcohol, or (even more facilely) treatment of the acid halide with alcohol in the presence of a non-nucleophilic base.
Facile reactions typically don't require a lot of work up or a lot of bother. At the risk of being stoned by the organic chemists in this community, I would not consider any reaction that involves subsequent use of chromatography for separation to be facile.
Combustion of hydrocarbons is certainly another example.