I think the first episode of last season, Kody talked about why they had trouble with regular jobs. I think he said that people have issues with them due to their high profile. I guess that if you are running a store you may not want it represented by a member of a publically known Plural marriage member. I would think Las Vegas would be open to things like that, but maybe not. Do prospective employers really hold it against them when hiring?
Also, I think that the money they can make at a regular job is peanuts compared to the TLC income. I'm just speculating.
I have another idea too. I wonder if the secret plural families give the Brown family funds to support them since they are helping the cause by going public. Many other polygamous famlies really cannot come out of the closet, for fear of reproach, such as doctors, lawyers, law enforcement, etc. Maybe they pay Kody to do what they are afraid to do. That could explain their unexplained income and why they don't want to discuss it.