Can Brago's ability keep Traft's angel token around?
If a token would leave the battlefield to any other zone it will cease to exist.


  110.5g A token that has left the battlefield can’t move to another zone or come back onto the battlefield. If such a token would change zones, it remains in its current zone instead. It ceases to exist the next time state-based actions are checked; see rule 704.


You can flicker your traft and brago and yes since they are entering the battlefield they would be untapped and also have summoning sickness. 

If you flicker a creature that's enchanted the enchantments would be removed and sent to the graveyard. Now if you flicker both the ward and the creature then I'm not sure but you might have to enchant another creature aside from the one re-entering since they enter at the same time and the enchantment wouldn't "see" the creature flickered along with it.