There are a number of issues:
figure is a floating environment. It is not placed directly but stored and placed where LaTeX thinks it fits best. This can be influenced by the optional argument like [H] but surrounding alignment environment still don't have any influence on it.
flushleft and flushright produce paragraphs and therefore a line break. So both contents will always vertical stacked, never side by side.
Note that you don't need a figure environment to use \includegraphics, only if you want a caption. Also you can have multiple images and captions (!) in one figure. Try the following code to place the two images side-by-side and at the left and right corner (if this is what you want):
\begin{figure}[H]
\includegraphics[width=107px,height=134px]{t1.jpg}%
\hfill
\includegraphics[width=113px,height=190px]{t2.jpg}%
\end{figure}
flushrightandflushleftare not standard latex environments. Are you loading some package or special documentclass that is providing them? – Lev Bishop Jun 21 '11 at 15:58\raggedleftand\raggedright. – Martin Scharrer♦ Jun 21 '11 at 16:02