The IEEEtrantools package which provides the IEEEeqnarray environment currently does not allow for the fleqn class/package option. You can, however, simulate the effect of this option by means of an adequate user-defined glue type:
\documentclass[fleqn]{article}
\usepackage{amsmath}
\usepackage{IEEEtrantools}
\IEEEeqnarraydefcolsep{0}{\leftmargini} % any number other than 0 also allowed as glue type
\begin{document}
\noindent
Text\hfill{}Text
\begin{equation}
x=1
\end{equation}
Text\hfill{}Text
\begin{IEEEeqnarray}{0rCl}
x&=&1
\end{IEEEeqnarray}
Text\hfill{}Text
\end{document}

This also works if the amsmath package is not present.
Note that the amsmath package defines a switch \if@fleqn. Using this switch you could redefine the IEEEeqnarray environment to automatically include the 0 glue type whenever the fleqn option is specified.