\documentclass{article}
\usepackage{siunitx}
\usepackage{dataplot}
\begin{filecontents*}{test.csv}
Label,Concentration,Rate
1,338.1,266.45
2,169.1,143.43
3,84.5,64.80
4,42.3,34.19
5,21.1,9.47
\end{filecontents*}
\DTLloaddb{data}{test.csv}
\begin{document}
\begin{figure}
\renewcommand{\DTLplotatendtikz}{%
\DTLforeach*{data}{\Conc=Concentration,\Rate=Rate,\Label=Label}%
{%
\draw (\Conc,\Rate) node[above left] {\Label};
}%
}
\DTLplot{data}{x=Concentration,y=Rate,
maxx = 400,