roundly vs flat out

roundly and flat out both are adverbs.

Word	Noun	Adjective	Verb	Adverb
roundly	No	No	No	Yes
flat out	No	No	No	Yes

As adverbs, roundly and flat out are synonyms defined as:

Other synonyms of roundly include bluffly, bluntly, brusquely.

roundly (adverb)	flat out (adverb)
in a round manner	in a blunt direct manner
in a blunt direct manner	at top speed