flirt vs chat up

flirt is a noun but chat up is not a noun.

Word	Noun	Adjective	Verb	Adverb
flirt	Yes	No	Yes	No
chat up	No	No	Yes	No

As verbs, flirt and chat up are synonyms defined as:

Other synonyms of flirt include butterfly, coquet, coquette, dally, mash, philander, romance.

flirt (noun)	chat up (noun)
playful behavior intended to arouse sexual interest
a seductive woman who uses her sex appeal to exploit men

flirt (verb)	chat up (verb)
talk or behave amorously, without serious intentions	talk or behave amorously, without serious intentions
behave carelessly or indifferently	talk to someone with the aim of persuading him