Android: Clear the back stack

intent.addFlags(Intent.FLAG_ACTIVITY_NEW_TASK | Intent.FLAG_ACTIVITY_CLEAR_TASK);
startActivity(intent);

Try adding FLAG_ACTIVITY_NEW_TASK as described in the docs for FLAG_ACTIVITY_CLEAR_TOP:

This launch mode can also be used to good effect in conjunction with FLAG_ACTIVITY_NEW_TASK: if used to start the root activity of a task, it will bring any currently running instance of that task to the foreground, and then clear it to its root state. This is especially useful, for example, when launching an activity from the notification manager.

So your code to launch A would be:

Intent intent = new Intent(this, A.class);
intent.addFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP | Intent.FLAG_ACTIVITY_NEW_TASK); 
startActivity(intent);
CurrentActivity.this.finish(); // if the activity running has it's own context


// view.getContext().finish() for fragments etc.