Center two images using multiple \hfills

An extra \hfill will do it. Also, \centering not needed in this case. And, technically speaking, one should end lines with % signs, in order to avoid the insertion of small spaces.

\documentclass{article}

\usepackage{graphicx}
\usepackage{blindtext}
\usepackage{float}
\usepackage{mwe}

\begin{document}

\blindtext

\begin{figure}[H]
%\centering
\hfill%
\includegraphics[width=4cm]{example-image-a}%
\hfill%
\includegraphics[width=4cm]{example-image-a}%
\hfill%
\hfill%
\end{figure}

\blindtext

\end{document}

Alternately (and more naturally), \hfil all around will do it with a single. However, in this case, \centering cannot be used, without the addition of an \hfilneg (negative infinite glue) at the beginning of the line (or else added asymmetric \hfils).

\documentclass{article}

\usepackage{graphicx}
\usepackage{blindtext}
\usepackage{float}
\usepackage{mwe}

\begin{document}

\blindtext

\begin{figure}[H]
%\centering\hfilneg
\hfil%
\includegraphics[width=4cm]{example-image-a}%
\hfil%
\includegraphics[width=4cm]{example-image-a}%
\hfil%
\end{figure}

\blindtext

\end{document}

Alternatively with \centering and \hfil between images:

\documentclass{article}
\usepackage{graphicx}
\usepackage{blindtext}

\begin{document}

\blindtext
\begin{figure}[htb]
\centering
\includegraphics[width=4cm]{example-image-a}
\hfil
\includegraphics[width=4cm]{example-image-b}
\end{figure}

\blindtext

\end{document}