siunitx does not work with overline

You can also set the number parsing off temporarily.

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

\begin{document}
\begin{align}
\begin{split}
s &= \frac{d}{t}\\
&= \frac{\SI{1.15}{m}}{\SI{1.43}{s}}\\
&= \SI[parse-numbers=false]{0.\overline{804195}}{m/s}
\end{split}
\end{align}
\end{document}

This does sort-of defeat the purpose of using siunitx, but it's possible with some box manipulation:

\documentclass{article}
\usepackage{siunitx,amsmath}% http://ctan.org/pkg/{siunitx,amsmath}
\begin{document}
\begin{align*}
    s &= \frac{d}{t} \\
     &= \frac{\SI{1.15}{m}}{\SI{1.43}{s}} \\
     &= \rlap{$\phantom{0.}\overline{\phantom{804\,195}}$}\SI{0.804195}{m/s}
\end{align*}
\end{document}

I've pre-set an invisible 0.804\,195 with a visible \overline (only over the necessary part) using a right overlap (a zero-width, left-aligned box). After this, \SI sets things as usual, this time "underneath" the \overline so it looks appropriate.