Microsoft just announced Continuum for Windows Phone 10 during the Build keynote...so I guess you have your answer. :-)
Lumia 640 does not support the minimum requirements for Continuum. The processor of Lumia 640 is an old chipshet. It does not require a phone that came preinstalled with the Windows 10 Mobile as said by @kelvinelove. Continuum was even demonstrated in a low end phone by a hacker. I don't have that link now. However the performance was terible. There is a ...
From: Windows Help - Set up Continuum for phones
Set up Continuum for phones
How you set up Continuum for phones depends on what type of hardware you’ve got. Here's what you'll need to get started.
(Click image to see animation)
A TV or monitor with HDMI input.
A Windows 10 Mobile phone that’s compatible with Continuum for ...
I'm gonna have to say "no", because, first off, the Lumia 640XL does not support Continuum.
Continuum is available on Windows 10 Mobile specific hardware, that is, phones that were designed specifically to work with Windows 10 Mobile as their initial OS. The Lumia 640XL supports Windows 10 Mobile, and can get it through an upgrade, but it doesn’t have the ...