Yes. You will be able to redownload any DLC you have purchased within the same console family. Any DLC you have purchased on Xbox 360 can be downloaded on Xbox One and any PlayStation 3 DLC can be downloaded on PlayStation 4.
If I buy DLC on a new console (PS4 or Xbox One), can I also download it for my previous system (PS3 or Xbox 360)?
No, but the opposite is true. If you want to own the DLC on both platforms within a console family, we advise you to buy it on the earlier console, then download it on the newer one.
Find out more information about Rocksmith 2014 in this dedicated forum post.
If you have any other questions, feel free to contact us.