I am having the exact same problem as describe in this question. Unfortunately, however, the solutions listed there do not seem to work for the multlined environment as well.
A MWE is the following.
\documentclass{article}
\usepackage{mathtools}
\makeatletter % This code works as
\newcommand{\AlignFootnote}[1]{% % a fix for multline
\ifmeasuring@ % environments, but
\else % not for multlined
\iffirstchoice@ % environments
\footnote{#1}%
\fi
\fi}
\makeatother
\begin{document}
\begin{minipage}{.5\linewidth}
\begin{equation}
\begin{multlined}
x=\AlignFootnote{This is a footnote.}0.
\end{multlined}
\end{equation}
\begin{multline}
x=\AlignFootnote{This is a footnote.}0.
\end{multline}
\end{minipage}
\end{document}
It seems as if this fix was only made to work for environments coming from amsmath, but not mathtools. Unfortunately, my TeXnichal skills are nowhere near good enough for me to be able to extrapolate this to a solution that also works for mathtools. Perhaps someone else more competent can see how to modify the fix (or just create a new one)?


multlineduses a very different model from the other alignment environments. For instance it also conflicts withsubstack, so it's not really a surprise it fails with other specificamsmathconstructs. – egreg Nov 07 '15 at 22:09multlinedmeasuring is actually setting\measuring@true– daleif Nov 12 '15 at 11:10multilineused inside a minipage – daleif Nov 12 '15 at 11:15the peculiar formatting of the
– barbara beeton Mar 06 '16 at 01:43multlineexpression is becausemultlineshould never be used with only one line. this wasn't intended, and probably never tested.