Or much easier, they could just provide "the Consent of the Congress,"  The Democrats, on January 10, 2017 submitted a proposed HJR denying that consent, of course.

They have granted consent many times over the years under the clause.   There is even a special law which permits retired military to receive compensation from foreign governments.   (37 U.S.C. § 908)

If you want a learned article from back in September when the question was raised that the clause might apply to Hillary  and the Clinton Foundation, it can be found at:

http://www.cleveland.com/opinion/index.ssf/2016/09/hillary_clintons_eligibility_t.html

Naturally, written by a liberal Professor Emeritus, the conclusion was that it would not apply to her.   

No doubt the Professor Emeritus will re-write the article in the near future to reflect his updated scholarly and unbiased  legal opinion based on the new facts.

There is no case law on the subject as it might apply to a President.