Stretching a curly bracket to get better vertical symmetry

I didn't get your MWE run through, but with a "regular" document class such as article it does run through. One standard trick is to add a \vphantom.

\documentclass[fleqn]{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
    \left\{
    \begin{aligned}
        a&=\frac{b}{c} \\
        a&=\vphantom{\frac{b}{c}}e
    \end{aligned}
    \right.
\end{equation*}
\end{document}

Note also that mathtools has several specialized commands/environments for similar scenarios, such as dcases.

Here are three possibilities:

\documentclass{article}
\usepackage{bigstrut}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
    \left\{
    \begin{aligned}
        a&=\frac{b}{c} \\
        a&=e\vphantom{\frac{b}{c_k}}%\\[-1ex]\mbox{}
    \end{aligned}
    \right.
\end{equation*}
\bigskip

\begin{equation*}
    \left\{
    \begin{aligned}
        a&=\smash[t]{\frac{b}{c}} \\
        a&=e
    \end{aligned}
    \right.
\end{equation*}
\bigskip

\begin{equation*}\setlength{\bigstrutjot}{2ex}
    \left\{
    \begin{aligned}
        a&= \frac{b}{c} \\
        a&=e \bigstrut[b]
    \end{aligned}
    \right.
\end{equation*}

\end{document}