Formatting units like 3k2 ohm with siunitx

I nominate

\SI[parse-numbers=false]{3k2}{\ohm}

and

\textup{3k2}\,\si{\ohm}

as answers to your question. The \textup directive guarantees that the numbers will be typeset in upright mode even when the expression occurs in italic text.

That said, I can't see what could possibly be wrong with writing

\SI{3.2}{\kilo\ohm}

Finally, if you really want to go for something eye-catching (though definitely also at least mildly eccentric), I could suggest

\SI{32}{\hecto\ohm}

\documentclass{article}
\usepackage{siunitx} % for \si and \SI macros
\begin{document}
\obeylines % just for this example
\SI[parse-numbers=false]{3k2}{\ohm}
\textup{3k2}\,\si{\ohm}
\SI{3.2}{\kilo\ohm}
\SI{32}{\hecto\ohm}
\end{document}

\documentclass{article}  
\usepackage{siunitx}
\newcommand\kohm[1]{\kohmaux#1\relax}
\def\kohmaux#1.#2\relax{\textup{#1}\SI{#2}[k]{\ohm}}
\begin{document}
\kohm{3.2}
\end{document}