The waiting to install message usually indicates the game is from a different region to your PSN accounts region,check the product ID code on the spine of the game case and compare to the ones listed in the link below.
http://www.gamefaqs.com/ps4/145061-call-of-duty-black-ops-iii/data
If it is a region mismatch issue the only way to get the DLC to install is to purchase the correct version for your region.