If the Yixlid Jailer enters the battlefield after Snapcaster Mage's ability resolves, the Jailer's effect will remove the flashback granted by the Mage.
To expand a bit: There is no practical way for them to make this happen. If a player drops a Snapcaster and understands timing, Jailer cannot realistically prevent them from flashing back the desired spell.
Scenario 1: It is your turn, and you resolve Snapcaster. If they respond to Snapcaster's ETB trigger, Jailer will resolve, then Snapcaster's ability. As Clariax explained, the triggered ability will have a later timestamp, and carry through in spite of Jailer. Alternately, if they wait for the ability to resolve, the stack will clear and you will gain priority. At this point, you can cast the spell (even if it is a sorcery) and it is too late for Jailer.
Scenario 2: It is your opponent's turn, and you resolve Snapcaster. They cannot respond to the ETB trigger, for the same reason presented earlier. If they wait for the trigger to resolve, then cast Jailer, you can simply flash back the targeted spell in response. The spell in question is presumably an instant (or you have Teferi/Vedalken Orrery/etc out), since you cannot typically cast sorceries in the opponent's turn.
I can't offhand think of a way for Jailer to stop you (unless you make a mistake that creates an window for the opponent to exploit).
