>when I process the file attached, I get arrows where they don't belong.
>Could somebody guide me to what I am doing wrong here?

I processed your chart. - There was no coloring.
I changed the following:

\setupFLOWcharts[background=color, backgroundcolor=klinik]

I grouped the 'sections' of the chart with \bgroup ... \egroup
Within the groups I was unable to use \setupFLOWcharts[background=color,
backgroundcolor=klinik]
so I used \setupFLOWshapes[background=color, backgroundcolor=labor]

When looking at the results, I realise that in the section
'Expressionsmessung' in the lower right corner appears a part of an arrow. I
believe, that this is inherent in the way the charts are set on a grid and
clipped later on. - Inevitable.

Grüße Willi