split inside flalign

You should be aware that flalign stands for full length align and not for flush left align.

As such, split doesn't really make sense inside it.

You can emulate split using aligned.

\documentclass{article}
\usepackage{amsmath}

\usepackage{lipsum} % for mock text

\begin{document}

\lipsum[1][1-3]
\begin{flalign}
\begin{aligned}
a1 & = 3534534343 \\
a2 & = 2342342  \\
a3 & = 4564564  \\
a4 & = 5845645645864596464  \\
a5 & = 345354  \\
a6 & = 1
\end{aligned}&&
\end{flalign}
\lipsum[2][1-3]

\end{document}

On the other hand, I see no reason for some displays to be flush left and others centered.

It is not very clear what you like to achieve, but the following solution may help you:

\documentclass{article}
\usepackage{nccmath}

\usepackage{lipsum}

\begin{document}
\lipsum[11]
\begin{fleqn} % defined in nccmath
\begin{equation}
\begin{split}
a1 & = 3534534343 \\
a2 & = 2342342  \\
a3 & = 4564564  \\
a4 & = 5845645645864596464  \\
a5 & = 345354  \\
a6 & = 1
\end{split}
\end{equation}
\end{fleqn}
\lipsum[12]
\[
c^2 = a^2 + b^2
\]
\end{document}

Environment \begin{flegn} ... \end{fleqn} (defined in nccmath package) locally align equation to the left (as do amsmath option fleqn for whole document).