If you like your objects and want to use flow, you can simplify it to get a result.

Make a copy of your organic fish shape.

Extract the surface from that copy that you want your gills on and discard the rest.

From the side view, create a closed curve big enough to encompass your gills and then trim the fish body extracted surface with it. Keep just the little shape.

Make a copy of that little shape and use the edit frame to "flat snap it".

Use ShrinkTrimmedSrf on flat and non flat pieces.

Then place your gill into the flat surface and use that as a base to flow to the non flattened piece.

Now the gill will place onto the fish in that spot.

Any "moving" needs to be measured so you can "move back" to initial place.

Let me know if this is unclear.