This is not possible. TestFlight will only accept apps signed with AppStore Distribution Certificate.
To distribute apps with Enterprise distribution profiles you must manage distribution yourself.
When you export an IPA from an XCARCHIVE using Xcode Organiser, you will see options to generate files (plists etc) that assist you in IPA deployment.
There are 3rd party platforms that enable Enterprise Distribution, for example Test Fairy, and until recently Microsoft App Center.
Topic:
App Store Distribution & Marketing
SubTopic:
TestFlight
Tags: