Here is a way that doesn't use the figure
environment but caption
package instead:
\documentclass[graybox,envcountchap,vecarrow,twoside]{article}
\usepackage[paperheight=240mm,paperwidth=170mm,top=2.5cm,inner=2.5cm]{geometry}
\usepackage[caption=false,font=footnotesize]{subfig}
\usepackage{graphicx}
\usepackage{lipsum}
\usepackage{caption}
%This code makes thhe whole job of vertical centering the image
% #1 includegraphics options
% #2 image name
% #3 image caption
\newsavebox{\mysavebox}
\newlength{\myvspace}
\newcommand\addCenteredImage[3][]{%
\clearpage
\savebox\mysavebox{\vbox{\phantom{.}\par\includegraphics[#1]{#2}}}%
\setlength\myvspace{\dimexpr(\paperheight-\dimexpr(\ht\mysavebox+\dp\mysavebox))/4\relax}%
\phantom{.}\vspace{\myvspace}\par\usebox\mysavebox\captionof{figure}{#3}\clearpage%
}
\begin{document}
% Some text
\lipsum[1-5]
% A figure in an new page
\addCenteredImage[height=10cm,width=10cm]{example-image-a}{This figure should be centered vertically}
\lipsum[6-10]
\end{document}
It is a way with simple commands as far as
I can understand them.
The output is the desired of your image.
Edit for subfigures: (After OP's edit)
\documentclass[graybox,envcountchap,vecarrow,twoside]{article}
\usepackage[paperheight=240mm,paperwidth=170mm,top=2.5cm,inner=2.5cm]{geometry}
\usepackage[caption=false,font=footnotesize]{subfig}
\usepackage{graphicx}
\usepackage{lipsum}
\usepackage{caption}
%This code makes thhe whole job of vertical centering the image
% #1 includegraphics options
% #2 image name
% #3 image caption
\newsavebox{\mysavebox}
\newlength{\myvspace}
\newcommand\addCenteredImage[1]{%
\clearpage
\savebox\mysavebox{\vbox{\phantom{.}\par #1}}%
\setlength\myvspace{\dimexpr(\paperheight-\dimexpr(\ht\mysavebox+\dp\mysavebox))/4\relax}%
\phantom{.}\vspace{\myvspace}\par\usebox\mysavebox\clearpage%
}
\begin{document}
% Some text
\lipsum[1-5]
% A figure in an new page
\addCenteredImage{%
\centering
\includegraphics[height=3cm,width=8cm]{example-image-a}
\captionof{subfigure}{Test 1}
\vspace{1cm}
\includegraphics[height=3cm,width=8cm]{example-image-b}
\captionof{subfigure}{Test 2}
\captionof{figure}{This figure should be centered vertically}
}
\lipsum[6-10]
\end{document}
Output:

\clearpage\null\vfil
with\begin{figure}[h]
? – Sigur Oct 16 '18 at 17:26