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%!TeX encoding = UTF-8 Unicode
\documentclass[12pt]{article}
\usepackage[]{geometry}
\usepackage{multicol}
%%%%%%%%%%%%%%%% the frames %%%%%%%%%%%%%%%%%
\usepackage[draft]{flowfram}
\newstaticframe[1]{150mm}{200mm}
{10mm}{10mm}[introduction]
\setallstaticframes{valign=t}
% add dummy flow frames to please the package
\newflowframe[1]{\textwidth}{0pt}{0pt}{0pt}
\newflowframe[>1]{\textwidth}{\textheight}{0pt}{0pt}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\setlength{\parskip}{2em} % this has no effect
\setlength{\parindent}{20pt} % neither does this
\begin{document}
\begin{staticcontents*}{introduction}
\setcounter{unbalance}{10}
\begin{multicols}{2}
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod
tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim
veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea
commodo consequat.
$$
\alpha = \beta
$$
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum
dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non
proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod
tempor incididunt ut labore et dolore magna aliqua.
\columnbreak
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod
tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim
veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea
commodo consequat. Lorem ipsum dolor sit amet, consectetur adipiscing
elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum
dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non
proident, sunt in culpa qui officia deserunt mollit anim id est laborum.
\end{multicols}
\end{staticcontents*} % end-introduction
\end{document}

I can't find anything to adjust the parskip, short of setting it explicitly inside every staticframe. I found that
\setlength{\sdfparindent}{2em}
can be used for the parindent, but I've had no luck finding something similar for parskip.