The words flack, flak sound the same but have different meanings and spellings. Why do flack, flak sound the same even though they are completely different words?
The answer is simple: flack, flak are homophones of the English language.
A press agent; a publicist.
To act as a press agent: flacking for a movie studio.
To act as a press agent for; promote: authors who tour the country flacking their books.
Variant of flak.
Antiaircraft artillery.
The bursting shells fired from such artillery.
Informal Excessive or abusive criticism.
Informal Dissension; opposition.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.
If they are spelled the same then they are also homographs (and homonyms); if they are spelled differently then they are also heterographs (literally "different writing").