How do I correctly align this equation?

I'm not sure there's anything to align, except for the two big braces. Don't force alignment to objects that aren't related to one another.

\documentclass{article}
\usepackage{amsmath,bm}

\newcommand{\cchi}{\mathord{\mathop{\bm{\chi}}}}

\begin{document}

\begin{align}
\max\eta_D(\mathbf{J}_{\cchi_{k,l}}) &\in (0,1]
\\
\text{subject to }
  &\left\{\begin{aligned}
        &\alpha_{12}^j \le \dfrac{\pi}{6}\\
        &\alpha_{23}^j \le \dfrac{\pi}{6}\\
        &\!\max_{\cchi\in\Omega}|\beta_1^j| \le \dfrac{\pi}{12} \\
        &\!\max_{\cchi\in\Omega}|\beta_2^j| \le \dfrac{\pi}{12} \\
        &\!\max_{\cchi\in\Omega}|\beta_3^j| \le \dfrac{\pi}{12} \\
        &\!\min_{\cchi\in\Omega}(\mathcal{D}_{\omega^j}) >0
  \end{aligned} \right.
\\
\text{bounded by } 
  &\left\{\begin{aligned}
        &{-}\dfrac{1}{12}\pi \le \varphi_1 \le \dfrac{1}{12}\pi\\
        &{-}\dfrac{1}{12}\pi \le \varphi_2 \le \dfrac{1}{12}\pi\\
        &0 \le \Theta_1 \le \dfrac{8}{45}\pi\\
        &0 \le \Theta_2 \le \dfrac{8}{45}\pi\\
        &0 \le \Theta_3 \le \dfrac{23}{180}\pi\\
        &(\varphi_1^j, \Theta_1^j) \ne (\varphi_2^j,\Theta_2^j) \ne (0,\Theta_3^j)\\
        &\varphi_2^j \ne 0
  \end{aligned}\right.
\end{align}

\end{document}

With dcases and nccmath for medium size fractions:

\documentclass{article}
\usepackage{nccmath, mathtools}
\usepackage{bm}
\DeclarePairedDelimiter\abs{\lvert}{\rvert}
\newcommand{\bchi}{\mathord{\mathop{\bm{\chi}}}}
\begin{document}
    \begin{align}
\max{\eta_D\left(\mathbf{J}_{\bchi_{k,l}}\right)} 
    & \in (0,1] \\
\text{subject to} 
        &   \begin{dcases}
            \alpha_{12}^j   \le \mfrac{\pi}{6}       \\
            \alpha_{23}^j   \le \mfrac{\pi}{6}       \\
            \max_{\bchi\in\Omega}\abs{\beta_1^j}   \le \mfrac{\pi}{12}   \\
            \max_{\bchi\in\Omega}{\abs{\beta_2^j}} \le \mfrac{\pi}{12}   \\
            \max_{\bchi\in\Omega}{\abs{\beta_3^j}} \le \mfrac{\pi}{12}   \\
\min_{\bchi\in\Omega}\bigl(\mathcal{D}_{\omega^j}\bigr) >0               \\
            \end{dcases}\\
\text{bounded by} 
        & \begin{dcases}
            -\mfrac{1}{12}\pi \le \varphi_1 \le \mfrac{1}{12}\pi\\ 
            -\mfrac{1}{12}\pi \le \varphi_2 \le \mfrac{1}{12}\pi\\ 
            0 \le \Theta_1 \le \mfrac{8}{45}\pi                 \\ 
            0 \le \Theta_2 \le \mfrac{8}{45}\pi                 \\
            0 \le \Theta_3 \le \mfrac{23}{180}\pi               \\
(\varphi_1^j,\Theta_1^j) \ne (\varphi_2^j,\Theta_2^j) \ne (0,\Theta_3^j)\\
            \varphi_2^j \ne 0
        \end{dcases}
    \end{align}
\end{document}