Hi Oliver, Flow works from one base surface to one target surface - when I say surface I mean just one surface, a "joined surface" is many surfaces joined together and the target can only be just one of those surfaces not the whole thing except for when you use "projective" mode for the Flow.

So in order to get what you want you will need to reconstruct the target object to be just one surface rather than a set of 3 separate joined together surfaces. To do that you will need to remove segmentation in any input curves you are using to construct the surface - if you do an extrude or sweep or something with a curve that is made up of multiple joined together segments, then the result will be multiple joined together surfaces as well.

So if you have a segmented curve you need to combine the segments together before using it to create the target surface. You could draw a new curve using Draw curve > Freeform > Control points that was just one long curve to do that, or also the Rebuild command can be useful for removing segmentation as well:
http://moi3d.com/2.0/docs/moi_command_reference10.htm#rebuild

- Michael