How to make a vertical \iff?

\Updownarrow is an extensible symbol, so you can use \Big in front of it.

\documentclass{article}
\usepackage{amsmath}

\newcommand{\Longupdownarrow}{\Big\Updownarrow}

\begin{document}

\begin{align*}
a+b&=c \\
\Longupdownarrow \\
x+y&=z
\end{align*}

\end{document}

You can do that with a \rotatebox:

\documentclass[11pt]{report}
\usepackage[utf8]{inputenc}
\usepackage{amssymb}
\usepackage{graphicx} 

\begin{document}

\[ A\mathrel{\mkern 3mu\rotatebox[origin =c]{90}{$\iff$}}B \]%

\end{document} 

Edit: as suggested by @egreg, you might consider using \Longleftrightarrow, which has a different spacing on each side (i.e. above and below after rotation):

\documentclass[11pt]{report}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amssymb}
\usepackage{graphicx} 

\begin{document}

\begin{gather*} 
    xxx yyyy zzz \\
A\mathrel{\mkern 3mu\rotatebox[origin =c]{90}{$\iff$}}B \\
 xxx yyyy zzz \\
 A\mathrel{\mkern 3mu\rotatebox[origin =c]{90}{$\Longleftrightarrow$}}B \\
    xxx yyyy zzz%
\end{gather*}

\end{document}