When Astral Dragon enters the battlefield, it and Flameshadow Conjuring trigger.
Resolve the Astral Dragon trigger, creating four token copies of Doubling Season that are 3/3 Dragon creatures in addition to their other types.
Resolve the Flameshadow Conjuring trigger, causing you to pay ({R} magic symbol) to create a total of 32 Astral Dragon tokens with haste.
When the Astral Dragon tokens enter the battlefield, they trigger, creating an extremely large number of Doubling Season tokens that are 3/3 Dragon creatures in addition to their other types.