unconvincing vs flimsy

unconvincing is not a noun while flimsy is a noun.

Word	Noun	Adjective	Verb	Adverb
unconvincing	No	Yes	No	No
flimsy	Yes	Yes	No	No

As adjectives, unconvincing and flimsy are synonyms defined as:

unconvincing (noun)	flimsy (noun)
	a thin strong lightweight translucent paper used especially for making carbon copies

unconvincing (adjective)	flimsy (adjective)
not convincing	not convincing
having a probability too low to inspire belief	lacking solidity or strength
	lacking substance or significance