It's quick and easy to enable closed captions on your Fire TV! There are two ways to do this: 

Option 1
1. With the CBS All Access app open, select "Settings". 
2. Scroll right to "CC Closed Captions".
3. Select "Display", and turn On.

Option 2
1. Select a CBS show. 
2. While the show is streaming, use the middle round button (menu button) on the Fire TV controller to bring up the video control.
3. Select the blue CC button.

Closed captions should now be enabled!