"GO TO NEXT CAPTION" Shortcut
You should be able to make a shortcut to go to next caption in the same way you can do with markers.

We have completely redesigned the captioning workflow in Premiere Pro version 15.0. You will see many dramatic workflow improvements. Please update to the latest version.
Learn all about the new captions workflow here: https://helpx.adobe.com/premiere-pro/user-guide.html/premiere-pro/using/working-with-captions.ug.html
-
Joe White commented
This still hasn't been resolved, so I've submitted a new request:
https://adobe-video.uservoice.com/forums/911233-premiere-pro/suggestions/44644059-go-to-next-caption-shortcutA simple solution would be to use tab and shift-tab to move between captions, as is the case in many other captioning tools.
-
Larson Scott commented
Yeah you should be able to do this. Has this been added yet?
-
Barnwell Elliott commented
@Adobe Staff - Nate,
I was referring to timeline. Using up / down arrows in timeline to just go to next caption instead of all cuts in timeline would be nice feature.
-
Adobe Staff - Nate commented
The up and down keys do this in the caption block. Are you referring to the timeline? If so this is an existing feature request. Thanks for reaching out.