You're lucky: \equiv
and \Rrightarrow
can be combined.
\documentclass{article}
\usepackage{amsmath,amssymb}
\makeatletter
\newcommand{\xRrightarrow}[2][]{\ext@arrow 0359\Rrightarrowfill@{#1}{#2}}
\newcommand{\Rrightarrowfill@}{\arrowfill@\equiv\equiv\Rrightarrow}
\newcommand{\xLleftarrow}[2][]{\ext@arrow 3095\Lleftarrowfill@{#1}{#2}}
\newcommand{\Lleftarrowfill@}{\arrowfill@\Lleftarrow\equiv\equiv}
\makeatother
\begin{document}
$A\xRrightarrow{fghi}B$
$A\xLleftarrow{fghi}B$
\end{document}

One can also add the symmetric version:
\documentclass{article}
\usepackage{amsmath,amssymb}
\makeatletter
\newcommand{\xRrightarrow}[2][]{\ext@arrow 0359\Rrightarrowfill@{#1}{#2}}
\newcommand{\Rrightarrowfill@}{\arrowfill@\equiv\equiv\Rrightarrow}
\newcommand{\xLleftarrow}[2][]{\ext@arrow 3095\Lleftarrowfill@{#1}{#2}}
\newcommand{\Lleftarrowfill@}{\arrowfill@\Lleftarrow\equiv\equiv}
\newcommand{\xLleftRrightarrow}[2][]{\ext@arrow 3399\LleftRrightarrowfill@{#1}{#2}}
\newcommand{\LleftRrightarrowfill@}{\arrowfill@\Lleftarrow\equiv\Rrightarrow}
\makeatother
\begin{document}
$A\xRrightarrow{fghi}B$
$A\xLleftarrow{fghi}B$
$A\xLleftRrightarrow{fghi}B$
\end{document}

\equiv
symbol could be tried. the technique should be derivable from the definition of\Longrightarrow
inamsmath.sty
, but i haven't got time to try it right now.