OK. So you're using triggered audio. Now I see the issue.
Closed Captioning text is only really compatible with slide audio, i.e. audio that has been added to the slide timeline like other objects. The only way you can synchronise the CC text to appear on cue is if the audio is locked to the frames on that timeline. Since you're triggering your audio to play by another method (Advanced Actions) there's no way to synch it with the default CC text method.
I still think your best bet is to use Captions to display synched text to your triggered audio as you can use the same Advanced Action that triggers the audio to SHOW the captions that display the corresponding text. However, what WILL be more problematic is getting those same captions to disappear again on cue. This is because the SHOW and HIDE actions must be triggered by events of some kind. So you might have to HIDE the previous CC caption when you trigger the next audio clip. Or if these are separate slides, then you could use the ON Slide Enter event to HIDE any captions that might still be present from previous slides.
Another option you have is to set up a user variables to hold the CC text and insert this variable into the caption that will display your dynamic CC text. Then you use your Advanced Actions to change the value of this variable, thereby changing the value of the text displayed in the caption. You still need to use screen events to drive all of this, but it's an option you might consider.