If the trust is not like a partnership, then the boot can be cashed out and taxed. Your partial 1031 exchange will be untaxed.
If a trust is like a partnership, this article details several solutions. This solution seems to be the simplest:
Having the partnership complete a 1031 Exchange, then refinancing the
acquired like-kind replacement property(ies) after a short period of
time and distributing the cash to partners who do not want to
participate in the 1031 Exchange transaction (buying back the
interests of those who want to cash out).
Other solutions mentioned in the article would require the trust to wait two years after the 1031 exchange before cashing your uncle out.