You shouldn't enclose the longtable in a center environment, because the table will be centered by default. Also, \label should go besides the \caption.
\documentclass{article}
\usepackage[margin=2cm]{geometry}
\usepackage{colortbl,longtable}
\usepackage{lipsum} % just for the example
\begin{document}
\lipsum[2]
\begin{longtable}{|c|c|c|}
\caption{Average Scalar Flux Groups 1 and 2 Test C}
\label{tlabel} \\
\hline
\rowcolor[gray]{0.85}\textbf{Average Scalar Flux Group 1}
&\textbf{Average Scalar Flux Group 2} & \textbf{Distance} \\
\hline
2.185692E-17 & 4.194769E-18 & 0.00 \\ \hline
-1.202652E-04 & 1.202652E-04 & 0.10\\ \hline
-2.405521E-04 & 2.405521E-04 & 0.20\\ \hline
-1.839872E-04 & 1.894445E-04 & 0.30\\ \hline
-1.295853E-04 & 1.403995E-04 & 0.40\\ \hline
-7.678566E-05 & 9.288239E-05 & 0.50\\ \hline
1.078685E-04 & -1.078685E-04 & 22.30\\ \hline
0.000000E+00 & 0.000000E+00 & 22.40\\ \hline
\end{longtable}
\lipsum[3]
\end{document}

Note that in the standard page setup for the article class the table is too wide, so it will stick in the right margin.
An even better result will be obtained with the help of the siunitx package that's able to format numbers in various ways. Note, in particular, that the hyphens in the preceding example should be minus signs.
\documentclass{article}
\usepackage[margin=2cm]{geometry}
\usepackage{colortbl,longtable,siunitx}
\usepackage{lipsum} % just for the example
\sisetup{
output-exponent-marker=\ensuremath{\mathrm{E}},
exponent-product={},
}
\begin{document}
\lipsum[2]
\begin{longtable}{
|S[table-format=-1.6e-2]|
S[table-format=-1.6e-2]|
S[table-format=2.2]|
}
\caption{Average Scalar Flux Groups 1 and 2 Test C}
\label{tlabel} \\
\hline
\rowcolor[gray]{0.85}\textbf{Average Scalar Flux Group 1}
&\textbf{Average Scalar Flux Group 2} & \textbf{Distance} \\
\hline
2.185692E-17 & 4.194769E-18 & 0.00 \\ \hline
-1.202652E-04 & 1.202652E-04 & 0.10\\ \hline
-2.405521E-04 & 2.405521E-04 & 0.20\\ \hline
-1.839872E-04 & 1.894445E-04 & 0.30\\ \hline
-1.295853E-04 & 1.403995E-04 & 0.40\\ \hline
-7.678566E-05 & 9.288239E-05 & 0.50\\ \hline
1.078685E-04 & -1.078685E-04 & 22.30\\ \hline
0.000000E+00 & 0.000000E+00 & 22.40\\ \hline
\end{longtable}
\lipsum[3]
\end{document}

You should also consider this possible enhancement, that avoids many problems both in readability and in horizontal spacing.
\documentclass{article}
\usepackage[margin=2cm]{geometry}
\usepackage{longtable,siunitx,booktabs}
\usepackage{lipsum} % just for the example
\sisetup{output-exponent-marker=\ensuremath{\mathrm{E}},exponent-product={}}
\begin{document}
\lipsum[2]
\begin{longtable}{
S[table-format=-1.6e-2]
S[table-format=-1.6e-2]
S[table-format=2.2]
}
\caption{Average Scalar Flux Groups 1 and 2 Test C}
\label{tlabel} \\
\toprule
\multicolumn{2}{c}{\textbf{Average Scalar Flux}} & {\textbf{Distance}} \\
\cmidrule{1-2}
{\textbf{Group 1}} & {\textbf{Group 2}} & \\
\midrule
2.185692E-17 & 4.194769E-18 & 0.00 \\
-1.202652E-04 & 1.202652E-04 & 0.10 \\
-2.405521E-04 & 2.405521E-04 & 0.20 \\
-1.839872E-04 & 1.894445E-04 & 0.30 \\
-1.295853E-04 & 1.403995E-04 & 0.40 \\
-7.678566E-05 & 9.288239E-05 & 0.50 \\
1.078685E-04 & -1.078685E-04 & 22.30 \\
0.000000E+00 & 0.000000E+00 & 22.40 \\
\bottomrule
\end{longtable}
\lipsum[3]
\end{document}
