\qed or \qedhere at the end of split environment

the best approach in this particular case is to use align*, as that behaves well with \qedhere since each line is treated separately. (any of the multi-line options that treats lines separately should work equally well.)

\documentclass{scrartcl}
\usepackage[fleqn]{amsmath}
\usepackage{amsthm,amssymb}

\begin{document}
\begin{proof}
...
\begin{align*}
        A&= B \\
         &= C\\
         &= D \qedhere
\end{align*}
\end{proof}
\end{document}

this isn't always ideal -- cases, for example, will always force the tombstone to the center vertically -- but the request has been made often enough to place the tombstone on the last line, that it should be considered as a possible option. i am adding it to the formal list of requests.

as noted elsewhere, with flush left equations and equation numbers on the right, there is a built-in conflict. that is why ams document classes default to using equation numbers on the left.

Here is what I'd do if I was using ntheorem instead of amsthm

\documentclass{scrartcl}
\usepackage[fleqn]{amsmath}
\usepackage{amssymb,bm}
\usepackage[ntheorem]{empheq}
\usepackage[amsmath,thmmarks]{ntheorem}
\theoremstyle{nonumberplain}
\theorembodyfont{\normalfont}
\theoremheaderfont{\itshape}
\theoremsymbol{\ensuremath\square}
\theoremseparator{.}
\newtheorem{proof}{Proof}
\begin{document}
\begin{proof}
...
\begin{empheq}{equation}
\begin{split}
A&= B \\
&= C\\
&= D
\end{split}
\end{empheq}
\end{proof}
\end{document}

This is a nice question! I guess that \qedhere is not designed for the purpose you want to achieve. I can only offer a workaround, and it's only simple if you have an odd number of lines. (Since for two lines you won't want to use it anyway, the problem starts with four lines.) The idea: Use the align environment with \nonumber instead of equation and split.

\documentclass{scrartcl}
\usepackage[fleqn]{amsmath}
\usepackage{amsthm}
\begin{document}
\begin{proof}
...
\begin{align}
        A&= B \nonumber \\
         &= C \\
         &= D \nonumber \qedhere
\end{align}
\end{proof}
\end{document}