Rain is more of trigger for many species in a dry desert environment.
In a location like the boreal forest - heat, humidity, and pressure fronts seem to dictate flight times.
For non-desert species, there also seems to be wider trigger as well, since many people report the same species flying on the same day despite being thousands of miles apart. Lasius neoniger for example, seems to fly across Canada and many places in the USA on the same few days.
Some species may have multiple flights throughout the year, such as Tapinoma sessile. This is more common in non-ideal conditions when a few alates decide to attempt the flight while others in the nest wait for another day or have not all eclosed yet.
Late June/early July always seem to be pretty slow as overwintered alates have flown and this seasons alates have not yet eclosed. Some species and some seasons make exceptions however.
Keep in mind that ants don't read these forums, and occasionally decide to set their own rules. Be prepared to be surprised regardless of how long you have been anting.