I can't see a way of profiling a deployed clickonce application, you will probably be better off profiling it before it's been deployed.
If you use the "install on the computer" option, it should be a matter of opening the program shortcut and using the shortcut program name and arguments in the memory profiler's .NET desktop application settings.
If you make it so your users always have to go through the web browser to run the application, this is a bit more tricky. I have tried a few things to make it work -- one was the obvious:
Then the less obvious way of running ClickOnce that I got from reverse-engineering it:
The ClickOnce app launches, but even with the "profile child processes" option turned on, neither ANTS Memory nor ANTS Performance profiler seem to pick up on the .NET app being run by ClickOnce.
I hope that someone more familiar with ClickOnce can chime in on this topic.