Take a look at the example here: http://docs.angularjs.org/api/ng.filter:filter
You can search by any of the phone properties by using
There are a bunch of good solutions here but I'd suggest going the other route with this. If searching is the most important thing and the 'secret' property is not used on the view at all; my approach for this would be to use the built-in angular filter with all its benefits and simply map the model to a new array of objects.
Example from the question:
$scope.people = members.map(function(member) {
return {
name: member.name,
phone: member.phone
}});
Now, in html simply use the regular filter to search both these properties.