Hey Chelsea Dickerson,
I had a look because I though this would a reasonably easy fix however I have had very little luck! I thought it might be a setting in the json that I could edit with ArcGIS Online Assistant but no luck.
You should be able to download the application and then change the icon in the index.html in the root of the application folder. It should be around line 9 and look like so:
<link rel="shortcut icon" href="images/shortcut.ico">
You will then need to host it using your own web server.
Thanks,
Ben
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