I ran into this bug today which was unfortunately closed as can't repro. I was renaming some AppSettings variable names (right click on a Project's  Properties and go to the Settings tabs) and deleting some other settings, when I did a Search/Replace for the entire solution and somehow wound up with a duplicate Settings.Designer.cs file named Settings1.Designer.cs. This was effectively a clone of Settings.Designer.cs which meant:

• IntelliSense would report that any AppSettings variables were declared multiple times
• The project wouldn't compile because the variables were already declared

The fix was to

• From the Error menu, double click the Settings1.Designer.cs file to open it. Right click on the file and select Open Containing Folder and backup the the offending file(s) first (just in case).
• After backing up, delete the Settings1.Designer.cs file
• Switch back to VS and ensure Show All Files is selected in the Solution Explorer
• Expand Settings.settings in the Solution Explorer and manually delete Settings1.Designer.cs (and if prompted say yes to removal from source control)
• Select Build...Clean Project... (or Solution as appropriate)

You should be good to go, if you get an error about a missing file, you may need to manually open your csproj or sln file in Notepad and ensure that the MSBuild script doesn't contain a link to Settings1.Designer.cs.