How to draw a labeled triple arrow (\Rrightarrow)

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}

Label over \Rrightarrow and \rightrightarrows. It is possible to use a triple arrows with TikZ macro: see this link Custom arrow shaft in tikz.

\documentclass[a4paper,12pt]{article}
\usepackage{amssymb, amsmath}
\begin{document}
\[a \stackrel{\text{label}}{\Rrightarrow}
 f\]
 \[a \stackrel{\text{label}}{\rightrightarrows}
 f\]
\end{document}