Spacing of \multline inside align (i.e. \multlined)

I can offer a quick fix for your \! problem, but I don't know if it has unwanted side effects. For some reason that I don't know, the definition of multlined contains

 \MH_if_boolean:nF {outer_mult}{\null\,}

in its internal macro \MT_mult_internal:n. It appears that this \, is the culprit! So to avoid the \,, you can set the boolean outer_mult "true". At least in your example, this has the desired effect that you don't need \! any more. Maybe the package maintainers can explain the role of outer_mult and its associated \,.

\documentclass{article}
\usepackage{amsmath,mathtools}
\MHInternalSyntaxOn
\MH_set_boolean_T:n {outer_mult}
\MHInternalSyntaxOff
\begin{document}
\begin{align*}
 & \left[k(k+\hbar),[k(k+\hbar),z]\right] \\
 & \qquad = 2[k(k+\hbar),m_yx-m_xy+i\hbar z] \\
 & \qquad = 2m_y[k(k+\hbar),x]-2m_x[k(k+\hbar),y]+2i\hbar[k(k+\hbar),z] \\
 & \qquad = 4m_y(ym_z-m_yz)-4m_x(m_xz-xm_z)+2\left\{k(k+\hbar)z-zk(k+\hbar)\right\} \\
 & \qquad = \begin{multlined}[t][10.5cm]
  4(m_xx+m_yy+m_zz)-4(m_x^2+m_y^2+m_z^2)z+{} \\
  +2\left\{k(k+\hbar)z-zk(k+\hbar)\right\} .
 \end{multlined}
\end{align*}
\end{document}

Looking into the mathtools documentation I found shortly after multlined the command \MoveEqLeft. It seems to help a lot in your case. You could do

\documentclass{minimal}
\usepackage{amsmath,mathtools}
\begin{document}
\begin{align*}
 \MoveEqLeft \left[k(k+\hbar),[k(k+\hbar),z]\right] \\
  & = 2[k(k+\hbar),m_yx-m_xy+i\hbar z] \\
  & = 2m_y[k(k+\hbar),x]-2m_x[k(k+\hbar),y]+2i\hbar[k(k+\hbar),z] \\
  & = 4m_y(ym_z-m_yz)-4m_x(m_xz-xm_z)+2\left\{k(k+\hbar)z-zk(k+\hbar)\right\} \\
  & = \begin{multlined}[t][10.5cm]
  4(m_xx+m_yy+m_zz)-4(m_x^2+m_y^2+m_z^2)z+{} \\
  +2\left\{k(k+\hbar)z-zk(k+\hbar)\right\} .
 \end{multlined}
\end{align*}
\end{document}

Unfortunately, as far as I can see, there seems to be no better solution with standard means like amsmath and mathtools. Of course if you would allow left alignment on the last line (of course with some more indentation), you could omit the nested environments altogether.