Will Yixlid Jailer negate Snapcaster Mage's flashback-giving ability?
Actually, in this scenario, if Yixlid Jailer was already on the field when Snapcaster Mage's "enter the battlefield" ability resolves, the card does have flashback until end of turn. This is mainly because, generally, when continuous effects that modify the same kind of thing (type, color, abilities, etc.), they are applied in timestamp order. Yixlid Jailer removes abilities, and Snapcaster Mage adds abilites, so when we consider how the effects are applied, first Yixlid Jailer removes all abilities of all cards in graveyards (because it entered the battlefield first), then Snapcaster Mage adds flashback to one card. So the net result is that that card has flashback.

If instead Snapcaster Mage's ability resolved first, it would give the card flashback and then Yixlid Jailer would remove the abilities, so the card would not end up with flashback. However, in most cases you can either cast the targeted spell in response to the Jailer or simply cast it before they have the opportunity to cast the Jailer (in the case where you cast Snapcaster on an empty stack and you are the active player).

The comprehensive rules say:


  
  613.1. The values of an object's characteristics are determined by starting with the actual object. For a card, that means the values of the characteristics printed on that card. For a token or a copy of a spell or card, that means the values of the characteristics defined by the effect that created it. Then all applicable continuous effects are applied in a series of layers in the following order:
  
  613.1f Layer 6: Ability-adding effects, ability-removing effects, and effects that say an object can't have an ability are applied.
  
  


and


  
  613.2. Within layers 1-6, apply effects from characteristic-defining abilities first (see rule 604.3), then all other effects in timestamp order (see rule 613.6). Note that dependency may alter the order in which effects are applied within a layer. (See rule 613.7.)
  613.6. Within a layer or sublayer, determining which order effects are applied in is usually done using a timestamp system. An effect with an earlier timestamp is applied before an effect with a later timestamp.
  
  
  613.6a A continuous effect generated by a static ability has the same timestamp as the object the static ability is on, or the timestamp of the effect that created the ability, whichever is later.
  613.6b  A continuous effect generated by the resolution of a spell or ability receives a timestamp at the time it's created.
  
  


One important thing to note is that Yixlid Jailer doesn't say "Cards in graveyards lose all abilities and can't have or gain abilities," so it doesn't stop the card from gaining flashback.