I suspect what you're looking for is a way to use the same copy of the blockchain and your wallet on disk, rather than creating a separate copy with the same keys. If you use the same software (and the same version, though it may work otherwise it could cause issues) on both operating systems, you can do this with a symbolic link; simply redirect the data directory or wallet file on one OS to the main copy on the other OS' partition. The commands you'll need are "ln -s" on Linux and "mklink" on Windows, though exact syntax depends on your environment (running the commands without parameters should give you some help text with more information). As always, make backups of both wallets before doing anything in case something goes wrong.
I used to dual boot, though Windows keeps screwing up the UEFI boot entry for my Debian partition and I now use a separate server for most things. Glad to see it's working well for someone, at least! :3