Your code and the logcat output you display are out of sync.
The error says that line 392 of your psupflip.java file you call addView, inside your inflate method, and you don't.
So I guess, you moved some code before getting the logcat.
The error may only come, in the code you show, from this line :
flipper.addView((View) LoadingScreen.viewInflate.get(i));
Chances are that you call this code several time with the same parameter. Thus, adding the same view twice to a view group. BUT, a view can have only one parent, you can't re-add to another parent like this, you must first remove it from its first parent view group (what logcat says indeed).
Try to stay closer to java naming conventions and learn how to read logcat errors, it will help you to go further in your development.
--UPDATE
Try this to remove the view from its parent :
View v = (View) LoadingScreen.viewInflate.get(i);
v.getParent.removeView(v);