I used to get an audible alert when I received Skype messages. For some reason now I don't. After checking all of the settings I could think of, it appears that it is turned on.
Have you tried rebooting?
Was the Skype app recently updated? If so, perhaps clearing the cache and/or clearing data for the app will work. If that doesn't help then uninstall and reinstall the app.
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My nexus 7 has been on kitkat a long time now so that shouldn't be the issue... Just did a power off and on cycle, no luck. The visual notification light works fine. Other sounds are working fine