"Can I get more than 1 Office 365 Personal Subscription if I have more than 1 qualifying device?
Yes, you can. You can redeem the offer for every new Lumia 640 or Lumia 735 phone you have purchased during the offer period.
Why can’t I get the Office 365 Offer?
This may be caused by the following reasons:
...
Your Microsoft account has already been used to activate the offer
..."
from:
FAQ ? Office 365 offer - Microsoft - USA
I interpret this to mean only one per account, but I'm going to try it with our second 640 later. If it works, I'll let you know.