Can I use Mr. Mime's "Trick" Attack to move a Team Flare Tool card from a Pokemon-EX to a non EX Pokemon?
Yes, and it would immediately go to its owner's discard pile.
Source: Primal Clash FAQ (2015-02-05), TPCi Rules Team (2015-02-05)

Relevant cards

Note: All applicable cards may not be listed below.
XY5_101