How to add vertical space after \hline without breaking vertical lines in a table

I suggest you drop the vertical line completely. How about something like this?

\documentclass{scrreprt}
\usepackage{setspace}
\usepackage[left=2.5cm,right=2.5cm,top=3cm,bottom=3cm]{geometry}
\usepackage{array,tabularx,booktabs}
\doublespacing

\begin{document}
\begin{table}[htb]
  \centering
  \onehalfspacing
  \caption{Table of info.}
    \begin{tabular}{@{}ccc@{}}
      \toprule
      Parameter & C/S Analyser & O/N/H Analyser \\
                & EMIA 320 V2 & EMGA 830 \\%
      \cmidrule(r){1-1}\cmidrule(lr){2-2}\cmidrule(l){3-3}
      Sensitivity (ppm) & 0.1 & 0.001 \\
      Furnace type & Induction & Impulse \\
      Carrier gas & Pure O2 & Pure He \\[0.1cm]
      \bottomrule
    \end{tabular}
  \doublespacing
  \label{tab:chem}
\end{table}
\end{document}

You can do that with the cellspace package: define a minimal vertical padding of rows, and prefix the relevant column specifier with the letter S (or C if you use siunitx):

\documentclass{scrreprt}
\usepackage{setspace}
\usepackage[left=2.5cm,right=2.5cm,top=3cm,bottom=3cm]{geometry}
\usepackage{array,tabularx}
\doublespacing
\usepackage{cellspace}
\setlength\cellspacetoplimit{5pt}
\setlength\cellspacebottomlimit{5pt}
\begin{document}

\begin{table}[htb]
  \centering
  \onehalfspacing
  \caption{Table of info.}
  \begin{tabular}{c | Sc c}
    \hline
                      & C/S Analyser & O/N/H Analyser \\
                      & EMIA 320 V2 & EMGA 830 \\
    \hline
    Sensitivity (ppm) & 0.1 & 0.001 \\
    Furnace type & Induction & Impulse \\
    Carrier gas & Pure O2 & Pure He \\
    \hline
  \end{tabular}

  \doublespacing
  \label{tab:chem}
\end{table}
\end{document} 

Add \\\\[-1.5\medskipamount] after \hline This will make one more row with small height.

The value before medskipamout should be chosen appropriately.