Placing the \closing command inside a minipage and the Attachments into another one will not produce, in general, the desired alignment, as can be seen in the following example:
\documentclass{scrlttr2}
\begin{document}
\begin{minipage}{.5\textwidth}
\closing{Kind regards,}
\end{minipage}%
\begin{minipage}{.5\textwidth}
Attachments\\
Att 1\\
Att 2\\
Att 3\\
Att 4
\end{minipage}
\end{document}
resulting in

which shows that the line "Kind regards," is not aligned with the "Attachments" line (using the optional argument for the minipages placement won't make things any better).
One possible solution is to use the minipages inside the \closing command:
\documentclass{scrlttr2}
\begin{document}
\closing{
\parbox{\textwidth}{\begin{minipage}[t]{.5\textwidth}
Kind regards,
\end{minipage}%
\begin{minipage}[t]{.5\textwidth}
Attachments\\
Att 1\\
Att 2\\
Att 3\\
Att 4
\end{minipage}
}}
\end{document}
The result:

EDIT: and the necessary modification for the signature:
\documentclass{scrlttr2}
\setkomavar{signature}{\hspace*{1.5em}My Name}
\begin{document}
\closing{\raggedright
\parbox{\textwidth}{\begin{minipage}[t]{.5\textwidth}
Kind regards,
\end{minipage}%
\begin{minipage}[t]{.5\textwidth}
Attachments\\
Att 1\\
Att 2\\
Att 3\\
Att 4
\end{minipage}
}}
\end{document}