All constants declarations are implicitly static, and the C# specification states that the (redundant) inclusion of the static modifier is prohibited. I believe this is to avoid the confusion which could occur if a reader were to see two constants, one declared static and one not - they could easily assume that the difference in specification implied a difference in semantics. Having said that, there is no prohibition on redundantly specifying an access modifier which is also the default one, where there is a choice. For instance, a (concrete) method can be explicitly marked as private despite that being the default. The rule appears to be that where there is no choice (e.g. a method declaration in an interface) the redundant modifier is prohibited. Where there is a choice, it's allowed.
I think "const" and "static readonly" are not the same. The "const" must be known at compile time. However "static readonly" is initialized at runtime, but its the value cannot be changed (because it's readonly) after initialization.
In practice, have a look at this example:
// Trying to assign an instance of a class StorageFolder (which can't be known at compile time) to FOO
// this will compile
private static readonly StorageFolder FOO = KnownFolders.DocumentsLibrary;
// this won't compile
private const StorageFolder FOO = KnownFolders.DocumentsLibrary;