Flying to Iquique in is usually considered the best time to fly. However, you will find other deals are always available year round. January tends to be the warmest period in Iquique so if you are looking for sun or warmer climates then look to fly around this time. November is the wettest if you need to factor this in to your plans.
What time of day is cheapest to fly?
At the moment, there are flights only in the morning for your Iquique trip.