Can I attach a Team Flare "Pokemon Tool F" card to my opponent's Pokemon-EX if it has the "Omega Barrier" Ancient Trait?
Yes, you can. The text of Omega Barrier says its effect excludes Pokemon Tools and Stadium cards.
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_151
XY5_24
XY5_60
XY5_77
XY5_86
XY5_9
XYP_XY49
XYP_XY49