The answer of the question:
Can I use same encryption key for both Windows and Ubuntu? is Yes. You can definitely use the same encryption key on both Windows and Ubuntu.
How part of the question requires some more info:
To use gpg key on Ubuntu
password and encryption keys and import your gpg private to the keystore.
then you can use this key to sign and encrypt files you want. Here is a good tutorial about using gpg on Ubuntu.
To use gpg on Windows
To use the same gpg key on Windows download a suitable tool from this site. After installation is complete you can import the gpg private key into your keystore and use that key to sign your files. The documentation is here