Flippant vs Glib

Although these words do overlap in meaning, there are differences. Wikidiff (reformatted) brings these out fairly well:

flippant [adjective]

• (archaic) glib; speaking with ease and rapidity: [Barrow] It becometh good men, in such cases, to be flippant and free in their speech.
• nimble; limber.
• Showing disrespect through a casual attitude, levity, and a lack of due seriousness; pert: [Burke] a sort of flippant , vain discourse // [2000, Anthony Howard and Jason Cowley, Decline and Fall, New Statesman] In the mid-1950s we both wrote for the same weekly, where her contributions were a good deal more serious and less flippant than mine. // [2004, The Easy Way to Stop Smoking]: Our society treats smoking flippantly as a slightly distasteful habit that can injure your health. It is not. It is drug addiction.

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glib [adjective]

• Having a ready flow of words but lacking thought or understanding; superficial; shallow.
• Smooth or slippery: a sheet of glib ice
• Artfully persuasive in nature: a glib tongue; a glib speech

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However, obviously, the senses are not listed in order of modern idiomaticity.

I'd say the default meaning of flippant is the third listed here,

• speaking with levity and a lack of due seriousness, and thus showing disrespect and a casual attitude

whereas the default meaning of glib is again the third, but informed by the others:

• artfully [cleverly / skilfully, especially in a crafty / cunning / slippery way] persuasive, having a ready flow of words