Correct me if I'm wrong, but I believe it only works in Doubles and Triples, where if both (or all 3) Pokémon use it in one turn, the power increases.
I am quite sure its not like Rollout or Fury Cutter where the power increases each turn you use it.
I think you're thinking of Round (an easy mistake to make since they're two similar sounding moves that no one uses). Round's power doubles from 60 to 120 when used by more than one of your Pokemon in a double or triple battle. On the other hand, Echoed Voice starts out at forty base power and increases by forty every consecutive turn it's used up to 200 power.