Would it really be possible to cook a fish in clay?
Baking fish in clay is like baking the fish in an impromptu duch oven: it keeps the moisture inside the meat, unlike roasting the fish on a skewer.

The clay should impart only very little flavour. If you use the clay directly on the fish, the skin typically sticks to the clay and is removed with the clay. Other methods wrap the fish in large leaves first and then in clay. Hay is also used occasionally, also for flavour. In all cases, the clay won't actually touch the bits you eat.

As for cooking times, this varies greatly, depending on


the size of the fish
the thickness of the clay layer
the heat and position in, on or next to the fire.


Sources vary from "ten to fifteen minutes on each side" (small trout in 1/2 inch of clay, right in the embers (1)) to "up to three hours" (2 inch thick clay layer, baked in heated stones and covered with soil (2)). The clay layer should be totally solid by the time the fish is done and depending on the type of clay, might show some cracks.