Farah says the word slightly differently than the Prince. Their discussion starts in this video at 4:10. The word is revealed at 4:20. I can hear a slight "m" undertone from Farah's ending that is absent in the Prince's pronunciation. He is consistent in the tomb and ending sequence in how he says the word. I don't know if Farah says it except for this one time.
https://www.youtube.com/watch?v=w0NDrbY6hV0
Two theories: One voice actor pronounced it correctly, the other didn't. Two, Farah's accent or the Prince's American accent is missing the sounds. There is no way to determine either as correct simply by listening. We would need the script and the game writer or director perhaps to confirm how to say this "nonsense" word.
For the purposes of a wiki, I think all spellings should be included as well as the different sound clips from Farah and the Prince. That would be thorough on the subject and the most complete. And further information from designers could be included as well if discovered.
I've seen it written only phonetically, but in several versions. It would be good to know which spelling the voice actors had in the script and any pronunciation direction from the sound booth.
Kakolookiyam, Kakolukeeyam, Kakolukiyam, Kakolukia, etc.