yesterday I needed to switch my old PSN Account off and created a new one. To make a long story short:
At this moment I didn´t think about the "one time" code usage of add-on activations. Is there any possibility to use an activation code twice (e.g. proof with pictures of codes etc.)?
If you're on PS4 and the DLC codes are yours, make sure your PS4 is activated as your primary and you should be able to load just fine.
If it's not activated as your primary, sign into the account, appear offline, then sign in to the other one and start Destiny.
Everything should be there.
I do this on my alternate account.