Perhaps you can try to Buffer the flow lines first with 500m and see where the buffer lines cross the flood plain polygons. You might need to use Feature To Line tool to convert the buffer polygons into lines and then use Intersect tool to analyze the crossings.
Once you know where the buffer crossing is, you can try to use those buffer polygons to select the flow lines. For these selected flow lines, try a smaller smoothing tolerance?
Having said the above, I actually wonder if you could smooth the flood plain polygons. Since you are allowing a significant change/reduction of accuracy for the flow lines, it may make sense to allow similar smoothing of the flood plain boundary to match the change in flow lines. That particular 90 degree corner (seemingly converted from a raster edge) could be smoothed away from the smoothed flow line.
Regards,