Cline not connecting fully in table with custom lines

The array package offers !{decl.} with <decl.> being used instead of the vertical line. To get a 1pt wide vertical line, you can use \vrule width 1pt. You can also declare a new column type based on this, using something like \newcolumntype{V}{!{\vrule width 1pt}}. (I used V instead of your original " here to avoid possible conflicts with the babel package since " is a shorthand in some languages.)

Instead of your definition of the \thickrule command, you could also use \Xhline from the makecell package. It accepts a width as its argument: \Xhline{1pt}

If you plan on using the thicker vertical and horizontal lines multiple times throughout your document, you might be interested in defining their widths in the pramble as I did in the following example.

In the following MWE, I also included a second version of your table that makes use of the booktabs package for a layout without vertical and wih less horizontal lines. There I also added the siunitx pacage in order to typeset units:

\documentclass{article}
\usepackage{array}
\usepackage{multirow}
\usepackage{makecell}

\newlength{\mytablinewidth}
\setlength{\mytablinewidth}{1pt}
\newcommand{\myhline}{\Xhline{\mytablinewidth}}
\newcolumntype{V}{!{\vrule width \mytablinewidth}}

\usepackage{booktabs}
\usepackage{siunitx}


\begin{document}

\begin{table}[h]
\centering
\begin{tabular}{|c|>{\centering\arraybackslash}p{1cm}V>{\centering\arraybackslash}p{1cm}|>{\centering\arraybackslash}p{1cm}|>{\centering\arraybackslash}p{1cm}|}
\hline
\multicolumn{2}{|cV}{\multirow{2}{*}{}} & \multicolumn{3}{c|}{Retort Diameter (mm)}             \\ \cline{3-5} 
\multicolumn{2}{|cV}{}                              & 750          & 1000           & 1200      \\ \myhline
\multirow{3}{*}{Gas Flow (SLM)}         & 25        & 5.7          & 3.2            & 2.2       \\ \cline{2-5} 
                                        & 50        & 11           & 6.4            & 4.4       \\ \cline{2-5} 
                                        & 75        & 17           & 9.6            & 6.6       \\ \hline
\end{tabular}
\caption{Approximate Peclet values}
\label{tb:Peclet}
\end{table}


\begin{table}[h]
\centering
\begin{tabular}{ccccc}
\toprule
                                                 &          & \multicolumn{3}{c}{Retort Diameter}   \\
                                                 &          & \multicolumn{3}{c}{(\si{\mm})}        \\
\cmidrule{3-5} 
                                                 &          & 750          & 1000           & 1200  \\ 
\midrule
\multirow{3}{*}{\makecell[cl]{Gas Flow \\ (SLM)}}& 25       & 5.7          & 3.2            & 2.2   \\  
                                                 & 50       & 11           & 6.4            & 4.4   \\
                                                 & 75       & 17           & 9.6            & 6.6   \\ 
\bottomrule
\end{tabular}
\caption{Approximate Peclet values}
\label{tb:Peclet2}
\end{table}


\end{document}

In addition to the ! trick already mentioned by leandriis, you can use the w column type that's much lighter codewise.

Also you could remove the empty rectangle at the upper left. But there are better ways to typeset the table, in my opinion, and I present one below.

\documentclass{article}
\usepackage{array,multirow}
\usepackage{booktabs}

\makeatletter
\newcommand{\thickhline}{%
    \noalign {\ifnum 0=`}\fi \hrule height 1pt
    \futurelet \reserved@a \@xhline
}
\newcolumntype{"}{!{\vline width 1pt}}
\makeatother

\newcommand{\smashedheader}[2][c]{%
  \smash{\begin{tabular}[t]{@{}#1@{}}#2\end{tabular}}%
}

\begin{document}

\begin{tabular}{| c | w{c}{1cm} " w{c}{1cm} | w{c}{1cm} | w{c}{1cm} |}
\cline{3-5}
\multicolumn{2}{c"}{\multirow{2}{*}{}} & \multicolumn{3}{c|}{Retort Diameter (mm)} \\
\cline{3-5} 
\multicolumn{2}{c"}{}                               & 750          & 1000           & 1200 \\
\thickhline
\multirow{3}{*}{Gas Flow (SLM)}         & 25        & 5.7          & 3.2            & 2.2  \\
\cline{2-5} 
                                        & 50        & 11           & 6.4            & 4.4  \\
\cline{2-5} 
                                        & 75        & 17           & 9.6            & 6.6  \\
\hline
\end{tabular}

\bigskip

\begin{tabular}{ @{} c w{c}{1.5cm} w{c}{1.5cm} w{c}{1.5cm} @{} }
\toprule
\smashedheader{Gas Flow \\ (SLM)} & \multicolumn{3}{c@{}}{Retort Diameter (mm)} \\
\cmidrule(l){2-4} 
          & 750          & 1000           & 1200 \\
\midrule
25        & 5.7          & 3.2            & 2.2  \\
50        & 11           & 6.4            & 4.4  \\
75        & 17           & 9.6            & 6.6  \\
\bottomrule
\end{tabular}

\end{document}