Formal:
* A barrage of complaints: This emphasizes the intensity and volume of the complaints.
* A chorus of complaints: This implies a unified and vocal group of complainers.
* An avalanche of complaints: This emphasizes the overwhelming nature of the complaints.
Informal:
* A storm of protests: This suggests a forceful and emotional outburst.
* A litany of grievances: This highlights the list-like nature of the complaints.
* A flood of criticisms: This conveys the sheer number and intensity of the complaints.
Figurative:
* A tempest in a teapot: This suggests that the complaints are disproportionate to the issue at hand.
* A powder keg: This implies a volatile situation that could easily erupt into conflict.
Ultimately, the best collective noun will depend on the specific context and the tone you want to convey.