There is actually a documented if little-known standard for escaping double quotes inside of double quotes for Win32 command lines. Programs that are written in C or use Microsoft's routine for parsing command lines into command arguments will follow that standard. Unfortunately, not all programs, even including programs provided by Microsoft, use Microsoft's code for parsing command lines into arguments nor even follow Microsoft's document rules.

Note that cmd.exe is still in the picture in most cases so not following Microsoft's rules can get you into minor trouble. You can produce a command that is incapable of receiving certain argument values. That is, if you want one of the things that cmd.exe takes care of for you (<, >, |, &, ^, etc.) included in a command-line argument, then you need to quote it in a way that cmd.exe recognizes. That way of quoting it would also need to be compatible with however the particular program chooses to parse its command line.

Anyway, the way you escape quotes inside of double quotes on Win32 command lines is to preceed them with a backslash. Unlike shell quoting, you can't just throw a double quote into the middle of an argument to start quoting there.

The specification is incomplete (lots of "behaviors that are undefined") and the implementation is at least a bit perverse which makes it appear quite buggy when one so quickly runs into the unspecified cases. The implementation may even be actually buggy for some cases that are within the specified limits, but I'm not aware of any such clear bugs. Quoting MS documentation:

Microsoft C/C++ startup code uses the following rules when interpreting arguments given on the operating system command line:

• Arguments are delimited by white space, which is either a space or a tab.
• The caret character (^) is not recognized as an escape character or delimiter. The character is handled completely by the command-line parser in the operating system before being passed to the argv array in the program.
• A string surrounded by double quotation marks ("string") is interpreted as a single argument, regardless of white space contained within. A quoted string can be embedded in an argument.
• A double quotation mark preceded by a backslash (\") is interpreted as a literal double quotation mark character (").
• Backslashes are interpreted literally, unless they immediately precede a double quotation mark.
• If an even number of backslashes is followed by a double quotation mark, one backslash is placed in the argv array for every pair of backslashes, and the double quotation mark is interpreted as a string delimiter.
• If an odd number of backslashes is followed by a double quotation mark, one backslash is placed in the argv array for every pair of backslashes, and the double quotation mark is "escaped" by the remaining backslash, causing a literal double quotation mark (") to be placed in argv.

There's also a library routine that does this parsing that can be used by programs not written in C, though I didn't spend the time trying to remember or find the name of it.