The Wall Street Journal has an editorial headlined "The Trump Family Political Business," recommending that President-elect Trump liquidate his holdings to eliminate concerns about conflicts of interest.
The editorial doesn't really get into the question, but it's certainly conceivable that Mr. Trump could take the position that if he goes ahead and does what the Journal is recommending, both he and his children would qualify for an exemption from capital gains taxes under 26 USC 1043, "Sale of property to comply with conflict-of-interest requirements."
A Forbes article from 2006 documents the way various cabinet officials in previous administrations have used the provision to avoid capital gains taxes.
The disclosure that Mr. Trump probably paid no personal income tax for some years because of a net operating loss carryforward was the subject of considerable press attention and political discussion during the presidential campaign. If that loss has expired, selling now would be a fine opportunity for Mr. Trump to avoid paying taxes on his gains.
Trump son-in-law and campaign adviser Jared Kushner has vast real estate assets that are separate from the Trump Organization, and if he were to join the administration, this provision might also be valuable to him.
Depending on how much capital gain is avoided, Mr. Kushner and Mr. Trump actually might, on an after-tax basis, do pretty well for themselves by using public service as an opportunity to divest some assets tax-free.