This is a know issue right now, and I'm sure the DICE team is working very hard to fix it.
I want to make everyone aware that you must go to the in-game store on the Battlefield 4 menu rather than the PSN because this is currently a Premium only DLC, and you may not be able to find it in the PSN Store.
If you aren't able to see the DLC in the store, try restarting your console, or un-installing BF4 from your console, and then re-installing it.
If the problem persists, please consider contacting a Electronic Arts Battlefield 4 technical support agent here: http://help.ea.com/en/contact-us/new/?product=battlefield-4
1) Pick the device you need help with.
2) Select the topic your problem falls under, and provide some more information on the issue.
3) Select 'Live Chat' or 'Call Me' depending on what is available, and what you would prefer.
Sorry for any inconveniences.