\text
用。。。来代替\rlap
。
\documentclass[fleqn]{article}
\usepackage{amsmath}
\begin{document}
\begin{alignat*}{5}
&\alpha &&:= 0\\
&\rlap{independant line with some $\alpha$ mathematics notation}\\
&\beta &&:= 1\\
&\rlap{random line}\\
&\sigma &&:= 2\\
\end{alignat*}
\end{document}