Wrapping or adding line breaks in header cell of siunitx's S-type column

You can nest any construct that allows linebreaking (a tabular or \parbox, or here I use \shortstack for a change)

\documentclass[12pt]{article}
\usepackage{siunitx, booktabs}
\sisetup{per-mode=symbol}
\setlength\parindent{0em}
\begin{document}
  \begin{tabular}{@{}cSSS@{}}
    \toprule
      &
      {\shortstack{Reaction 1\\(\si{\mmol\per\s})}} &
      {\shortstack{Reaction 2\\(\si{\umol\per\minute})}} &
      {\shortstack{Reaction 3\\(\si{\pmol\per\hour})}} \\
    \midrule
      Item 1 & 10 & 12 & 15 \\
      Item 2 & 20 & 22 & 25 \\
      Item 3 & 30 & 32 & 35 \\
    \bottomrule
  \end{tabular}

\end{document}