The minimum slope can be flat and the side slopes must be stable and perhaps mowable, 3:1 to 5:1.

Here in Minnesota there is actually a ditch authority, generally overseen by each county.  Just a thought if you are planning a future system ~ develop a large wetland buffer that field drainage runs through prior to entering waterways.  This will trap much of the silt and dirt, and the plants that will naturally establish themselves in the presence of water will soak up much of the nutrients that you do not want to get into the waterway.  This has been a huge problem in Minnesota.  We've destroyed our natural water resources in the name of expanding agriculture.

If you do like ornerynorsk says, suggest you consider a maze alignment - back and forth and back and forth - you get a much longer path for deposition of silts etc for the same area of "wetland".