If 2 copies of Gleam of Authority are on the board would that mean that +1/+1 counters would bounce back and fourth to infinity?
No, it would not.
You misunderstood how Gleam of Authority works. Gleam does not place +1/+1 counters on the creature it enchants, it simply gives it +1/+1 for each counter on other creatures. The difference is that counters remain on the permanent they are placed on while the +1/+1 granted by an enchantment disappears when the enchantment is destroyed.