I am creating a clickonce installer for my wpf application from within Visual Studio 2013 Community edition. This application uses a localdb. It works fine on the target machine
I'm having exactly the same problem as well. I found one potential answer at the MSDN forum and it seems to work for me.
To summarize the answer from the link: You have to create a "bootstrapper" for LocalDB 2014. This is just a folder in your "Microsoft SDKs directory" containing some specific xml files with keys/meta-data and an eula text file. The answer in the link provides the content for these xml files. After restarting visual studio, "Sql Express 2014 LocalDB" will appear along with all the other prerequisites and can be added to ClickOnce dependencies.