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The spell checker is a part of the regular VC++ IntelliSense engine. It is less accurate then the Clang-based IntelliSense provided by VisualGDB, and only works with MSBuild and GNU Make projects (not advanced CMake). You can switch between Clang Intellisense and regular VC++ IntelliSense as shown here.
Another option would be to enable the Clang’s spell checker by adeding “-fspell-checking” to VisualGDB Project Properties -> IntelliSense Settings -> Additional flags for C/C++ files, and also to the RelevantCFLAGS field in %VISUALGDB_DIR%\CppEngineTuningInfo.xml. That said, there is very little information available on Clang’s spell checker, and it doesn’t seem to be very popular.
Yet another option would be to use a stand-alone command-line spell checker, and create a custom shortcut to run it (VisualGDB Project Properties -> Custom Shortcuts). This way you could run it via a menu command in Visual Studio or the VisualGDB toolbar.