The Flash Rotating Logos are completely optional. You don't even have to have flash installed to run RR if you don't want to use any flash objects.
There are three ways to make the flash logo stop:
1-Look for a replacement flash logo that doesn't spin -- there are some skins that provide stationary logos that do not spin, and that show a clock when clicked. Those are still FLASH logos, they just don't spin. You can simply replace the logo.swf of your current skin with the swf file of the logo of your choice and it should be replaced for you automatically. You can also make your own .swf logo file in flash if you rather do that (requires Flash and some skills). You can of course look for other spinning logos of your choosing to replace the current one in the skin.
2-Remove the flash logo and replace it with a regular Image. You can download a few GIF logo files HERE, then all you have to do is open your menu.skin file (in your skin's folder) and find this line:
and change it for this:
Then copy the GIF logo of your choice into your skin's folder with the name "logo.gif" and RR should automatically load the logo file for you. You can play around with the XXX numbers to position/size the logo to your liking (read skin commands.txt for details).. remember that if you resize the skin, the looks of the logo may also change. If you don't like the GIF logo provided (or if the brand you want is not provided) you can always just make a GIF file with transparency and save it as logo.gif in your skin's folder.
3-Edit the xxxx_Empty.JPG of the skin you're using to include the logo of your choice -- this requires some graphics editing skills (to look good), but even MS Paint could work. RR will automatically use the files you replace on your skin's folder as long as you save them with the same name and on the same place/format. Then if you don't want the flash logo to display on top of your drawing/image, just delete the logo.swf file on your skin's folder.