I have grazed my kune kune within my sheep field, but enclosed by electric fence within that. They do graze, but if it's wet and muddy or they don't have enough grazing, they can turn the ground over. It is ideal to have several smaller paddocks that you can rotate around to allow the grass to grow back after they have grazed it for a while. I have pig arks for them to sleep in, they can then be moved from paddock to paddock if you need.
If your stock fencing is strong and well buried then it may keep pigs in, but they can root around the edges and lift the fencing to get under. A single strand of electric at nosing height can help. Or I use two strands up to about knee high to make a full enclosure.
As advised, pig feed is very high in copper so toxic to sheep. There are other things like ewe rolls or universal stock rolls that can be fed to both, but can be less than perfect nutrition for either species so I would advise making sure the pigs can be fed somewhere the sheep can't go.
The rough rule of thumb for feeding kunes is a pound of feed per pig per day, but this can go up if not much grazing or in winter, or reduced if they are getting a lot of grazing/browse through the summer and/or are overweight!
I usually find they are ready for slaughter around 12-18 months depending on individual growth and how big a carcase you are hoping for.
Hope that helps, feel free to ask any more questions. The British kune kune pig society has a website with lots of useful information, lists of breeders and recently birth notified piglets available for sale (I have a litter that is nearly 2 weeks old near St Cyrus if you are nearby and wanted to see my setup)