It will all depend on where you are salt was as valuable as gold and used as money in some places and not all that long ago.
Salt is still a major resource in many places today.
If you are going to try to extract salt from plants or trees you need to know the complete chemical makeup remember that cyanide can also be extracted from plants, in fact it is a form of salt.
Areas that have natural salt deposits are great if you happen to be in one. As someone said follow the animals to see where they are getting salt.
Clay is just wet dirt, silt, it won't necessarily have a high enough salt content to be of any use. If the surrounding area doesn't have salt the clay won't either.
If the clay does have salt, and you are sure it doesn't have things you don't want, you can consume it without chewing on it. Even if you are sure it has salt be careful. Try a very small amount to see if you have any ill effects.