1. "Flack" as a noun, meaning "publicity" or "press agent":
* This is spelled "flack".
2. "Flack" as a verb, meaning "to promote" or "to publicize":
* This is also spelled "flack".
3. "Flak" as a noun, meaning "anti-aircraft fire" or "criticism":
* This is spelled "flak".
Therefore, the correct spelling depends on the context.