Nope. Things do only what they say.
Illusionist’s Bracers says:
whenever you cast a cantrip, you can use a bonus action on the same turn to cast that cantrip a second time.
It does not say that it makes any exception to the normal concentration rules and allow you to concentrated on more than one cantrip at a time, so you can’t as per page 203 of the PHB:
You lose Concentration on a spell if you cast another spell that requires Concentration. You can’t concentrate on two Spells at once.