Doesn't look like Dragon Diction has a built in print feature.
However it should be easy enough to copy and paste the note into another app that does.Tap the top right icon (down arrow with bar) and choose copy. Then open your favorite note/text app that has printing and paste the text into a new note, and print.
Another option is email. I've got an Evernote account. It comes with an email address that you can send notes to. Once it syncs with Evernote I can print the note, among other organizing, syncing, searching, and editing options.
Or, you could just email it to yourself and print from the Mail app.