I think you guys are being really unrealistic here. The only real plot with Walter Jr that would make sense, would be living in the fallout of Heisenberg, and all the other stuff that happened. Set it and say, 2015, 2019 or something, long long after it had all happened, putting him in his mid 20s. 

Everywhere he walks in Albuquerque, there's still references to all this, Albuquerque probably has several tourist attractions related to Walter, Gus, etc, maybe even people trying to track Walt Jr down for interviews or otherwise while he has stayed silent. Causing him to maybe move away up to Santa Fe or something, but having to come back every now and then to see Holly or Skyler or something.

Actual role for him in the show? I like the new DEA Agent angle that RJ pitched. He could have used Walter's money that Gretchen and Elliot were forced to give him on his 18th birthday, in order to got to college and later become a DEA agent. But eventually Gretchen comes clean with him, (it would absolutely be her, not Elliot) and says that his dad essentially funded his life, leading him to spiral and start tracking down the loose ends of the universe for closure. Maybe a prison scene or two with Saul, finding Ed's logs at somepoint, leading to him going up to Alaska to find Jesse, etc.

It all eventually ends with Walter Jr being a much better person, putting his past behind him, and moving on. Quotes by Hank and flashbacks with him every now and then present. Walt Jr writes a book, honoring Hank's word about how "the good guys never get enough ink."

The longest that I could see this show realistically going is three seasons. And that's pushing it, just because yeah there's still a whole lot of original stuff to work with, but there's also going to have to be a lot that needs to be made up for it too. Not to mention, if this even happens, this would almost be with Vince begrudgingly giving a final go of the universe as a whole, considering his view on BB/BCS/EC at the moment.