As Michael explained, the flow depends on how the destination surface has been made.

You can see how it will react with the function "Show Pts"





Next, if you want a same border everywhere (without it inflates during flow), you have to do it after flowing with an offset function for each piece.

There is another method but much longer to have more curvy result near network method.
- do the median curve (iso or cmorph process)
- Use a array/curve on a base line with the median curve.
- fix the size of segments to be on the curves
- loft the segments to have the destination surface

You loft and offset your pieces next






The Show Pts gives this

For any other users that might encounter the same problem.

In the end I split it in smaller blocks and flowed the design individually.
It came out perfect! and went pretty quick.

Thanks to all.