It shouldn't matter if you wanted to access that class via css:
div.conversationCard-phone{
//css stuff
}
I'm not sure why you're using the ability to specify attributes in your css for classes, the method I've described is the common way of doing it. Can you perhaps elaborate on why you're using the attribute selector?
Edit
Change your html to
<div ng-repeat="message in data.messages" ng-class="message.type" class="conversationCard"></div>
So that processed it becomes
<div ng-repeat="message in data.messages" ng-class="message.type" class="ng-scope conversationCard phone"></div>
So in your css you can do
div.conversationCard{
//css stuff
}
And if you want to isolate the phone one:
div.conversationCard.phone{
//css stuff
}