flare up vs burst out

flare up and burst out both are verbs.

Word	Noun	Adjective	Verb	Adverb
flare up	No	No	Yes	No
burst out	No	No	Yes	No

As verbs, flare up and burst out are synonyms defined as:

Other synonyms of flare up include break open, erupt, flare, irrupt.

flare up (verb)	burst out (verb)
erupt or intensify suddenly	erupt or intensify suddenly
ignite quickly and suddenly, especially after having died down	give sudden release to an expression
	appear suddenly or unexpectedly; happen unexpectedly