How long to store slow-cooked chicken in liquid in fridge?
Assuming it has been treated appropriately in all other ways (not being left out at in the "danger zone" of 40-140 F / 4-60 C for more than about two hours commulative over the entire life time, raw and cooked)) cooked chicken should last 3-4 days in the refrigerator.

See for example, the example of fried chicken per South Carolina's Department of Health and Environmental Control.  It is the only example of cooked chicken in the list, but should be well representative.  Similarly, Still Tasty advises 3-4 days on chicken broth, which would represent the juice or gravy&mdash;they indicate the same for chicken Parmesan.  

You may be noticing a trend here: all chicken based dishes have about the same storage lifetime.

The fact that it is stored with the juice or gravy, or that you cooked it in a slow cooker is not really important.