This solution uses standard LaTeX/TeX commands.
How this works, whether using wrapfig or any other package, is that you are overlaying the image on the page, then preventing the text from overlapping this image. \rlap overlaps horizontally and \raisebox can be used to overlap vertically. \strut is used here mostly because it is easier to type than \leavevmode.
In this case, the text doesn't overlap the image without modification. However, by setting and resetting \rightskip you can protect the right size of the page from longer lines (at least inside flushleft). The limitation is that you can only do this between paragraphs.
\documentclass[a4paper,12pt]{article}
\usepackage[showframe]{geometry}
\usepackage[demo]{graphicx}
\begin{document}
\begin{center}
{\LARGE Stagewerkplan over het onderzoek naar}\\[0.1cm]
\LARGE{\textit{``Ricochetbeschadiging op beton''}}
\vspace{2cm}
\includegraphics[scale=1.4]{Politie_Logo.pdf}
\end{center}
\vspace{50mm}
\begin{flushleft}
\textbf{Student:}\\ \textit{Emiel Janssen}\\
\textbf{Studentnummer:}\\ \textit{349226}
\textbf{Stagecoördinator:}\\ \textit{Joost Hansté;\\
Senior Wetenschappelijk Forensisch Onderzoeker}
\rightskip=\dimexpr 5.5cm+\columnsep\relax% not needed in this case
\strut\rlap{\makebox[\textwidth][r]{\raisebox{\dimexpr \ht\strutbox-\height}[0pt][0pt]
{\includegraphics[width=5.5cm]{Saxion_logo.pdf}}}}%
\textbf{Organisatie}\\ \textit{Politie Oost-Nederland\\
Afdeling Forensische Opsporing\\
Hermandad 2\\
7511 JN Enschede}
\rightskip=0pt
\textbf{Stagebegeleider:}\\ \textit{Drs. Maria Berk}
\end{flushleft}
\end{document}
It occurred to me that you might be trying to bottom align the text and image.
\documentclass[a4paper,12pt]{article}
\usepackage[showframe]{geometry}
\usepackage[demo]{graphicx}
\setlength{\parindent}{0pt}%
\begin{document}
\begin{center}
{\LARGE Stagewerkplan over het onderzoek naar}\\[0.1cm]
\LARGE{\textit{``Ricochetbeschadiging op beton''}}
\vspace{2cm}
\includegraphics[scale=1.4]{Politie_Logo.pdf}
\end{center}
\vfill
\hangindent=\bibindent
\textbf{Student:}\\ \textit{Emiel Janssen}
\hangindent=\bibindent
\textbf{Studentnummer:}\\ \textit{349226}
\hangindent=\bibindent
\textbf{Stagecoördinator:}\\ \textit{Joost Hansté;\\
Senior Wetenschappelijk Forensisch Onderzoeker}
\setlength{\rightskip}{\dimexpr 5.5cm+\columnsep}% not needed in this case
\hangindent=\bibindent
\textbf{Organisatie}\\ \textit{Politie Oost-Nederland\\
Afdeling Forensische Opsporing\\
Hermandad 2\\
7511 JN Enschede}
\hangindent=\bibindent
\textbf{Stagebegeleider:}\\
\strut\rlap{\makebox[\dimexpr \textwidth-\bibindent][r]{\smash{\includegraphics[width=5.5cm]{Saxion_logo.pdf}}}}%
\textit{Drs. Maria Berk}
\setlength{\rightskip}{0pt}%
\end{document}

\documentclassand ending with\end{document}. - aybe helpful How to place an image at the right top of a document – Bobyandbob Sep 19 '18 at 08:13