It was supposed to happen today. Many trainers have spent time, energy, and Stardust powering up their Flying-type Pokémon to perfect their teams for this very night. However, in the eleventh hour, Niantic posted that, alas, tonight's GO Battle Night and Flying Cup have been postponed.
The GO Battle Night was set to debut the Flying Cup tonight, which only allowed Flying-type Pokémon to enter. The night would allow 100 PVP battles and would offer Shiny-capable encounters with Pidgey. When evolved up to Pidgeot during the event's hours, the Pokémon would know the exclusive move of Gust. This was meant to tie into Mega Pidgeot's current release, but major glitches in the GO Battle League have forced Niantic's hand. It's probably the correct move, but it's also a shame how close the announcement came to the event after trainers invested time and effort into developing something as niche as a team of Flying-type Pokémon with CP under 1500.
The Halloween Cup seems to be unaffected by this, and per Niantic's October 2020 announcement today, will continue as planned.
Previous postponed events include the Lugia Raid Weekend, which was set to give the iconic Legendary Pokémon the exclusive move Aeroblast. This was delayed due to the beginning of the COVID-19 lockdown. Since then, Niantic has done multiple different raid rotations with no delay, and no word of when Lugia will get its time to shine. Because of this, it's advisable not to hold your breath waiting for the rescheduled GO Battle Night and Flying Cup. It'll be nice if it happens soon but, as Lugia's absence is drawn out longer and longer, there's not much reason to put stock in Niantic's timeline for "postponed" events.