OK, so first things first. This tablet has two handwriting modes: One that kicks in automatically in text fields (the little pencil pop-up that shows when you hover over the text field) or the one built into the Samsung Keyboard (the pen option on the settings key). The first shows up regardless of the keyboard you're using and the latter works only in Samsung Keyboard.
That being said, for some reason, some fields are NOT being recognized as text ones. E-Mail, unfortunately, seems to be one of them, so the first handwriting mode doesn't kick in and doesn't show the option to use it. SwiftKey, unfortunately, has no handwriting recognition mode, so unless they add that in a future version, you're out of luck (what I do is I just change keyboards when I need handwriting mode, go back to SwiftKey when I'm done).