You can do it. But don't abuse flalign.
\documentclass[fleqn,leqno]{article}
\usepackage{amsmath}
\usepackage{lipsum} % for context
\makeatletter
% from https://tex.stackexchange.com/a/261647/4427
% detach \eqref and \tag making
\renewcommand{\eqref}[1]{\textup{\eqreftagform@{\ref{#1}}}}
\let\eqreftagform@\tagform@
% specific code for the question
% 1. define a new tag form for subequations
\newcommand\subtagform@[1]{%
\maketag@@@{%
\ifx#1\theequation
\ifnum\value{equation}=1
(\theparentequation)%
\else
\phantom{(\theparentequation)}%
\fi
\ \alph{equation}.%
\else
\ignorespaces(#1\unskip@@italiccorr)%
\fi
}%
}
% 2. tell LaTeX to use the new tag form
\AtBeginEnvironment{subequations}{\let\tagform@\subtagform@}
\makeatother
% you need bigger left margin
\setlength{\mathindent}{4em}
\begin{document}
\begin{subequations}\label{test}
\lipsum[1][1-4]
\begin{align}
1&=1 \label{test-a}\
2&=2 \label{test-b}
\end{align}
\lipsum[1][1-4]
\end{subequations}
\eqref{test}, \eqref{test-a}, \eqref{test-b}
Now a standard equation
\begin{equation}
3=3
\end{equation}
\end{document}
