How to define a fixed spacing between characters independent of font-size?

Set it up to account for the math style.

\documentclass{article}
\newcommand\dblA{\mathchoice
{A\hspace{-.7ex}A}
{A\hspace{-.7ex}A}
{A\hspace{-.58ex}A}
{A\hspace{-.55ex}A}%
}
\begin{document}
$\dblA AA$

$\scriptstyle\dblA AA$

$\scriptscriptstyle\dblA AA$
\end{document}