I tested this and was able to change the initial loading icon but when the icon appears again like when you make a filter change, I was not able to change that one.
For the initial loading icon, replace the 30x30REV.gif icon that is located at C:\Program Files\Tableau\Tableau Server\8.x\wgserver\public\images.
I would think the other loading icon is C:\Program Files\Tableau\Tableau Server\8.x\wgserver\public\v_BUILDNUMBER\images\loading.gif but changing this did not work.
Be sure to restart Tableau Server after replacing the icons (be sure to use the same file name and extension).
Also, this is very unsupported and will revert back upon upgrading Tableau Server
I know, its been so long, but this thing is not working for me Tableau server 10. I want to change the Loading Image which pop up whenever opens a report on server. I tried to find the same .gif file in tableau server folder but ended up in failure.
Suggestions are most welcome from anyone