You should be able to do this,
To write to a shared object
//returns the mySharedObject if it exists, if not creates a new one
var so:SharedObject = SharedObject.getLocal("mySharedObject");
//take your array and put it on the so
so.data.storedArray = myArray;
//save the data
so.flush();
To read it back elsewhere
//get the mySharedObject back
var so:SharedObject = SharedObject.getLocal("mySharedObject");
//get your array back
myArray = so.data.storedArray;