Can multiple Thorncaster Slivers grant multiple copies of the same ability?
Yes, they will have two copies of the ability:


  112.2c An object may have multiple abilities. If the object is represented by a card, then aside from certain defined abilities that
  may be strung together on a single line (see rule 702, “Keyword
  Abilities”), each paragraph break in a card’s text marks a separate
  ability. If the object is not represented by a card, the effect that
  created it may have given it multiple abilities. An object may also be
  granted additional abilities by a spell or ability. If an object has
  multiple instances of the same ability, each instance functions
  independently. This may or may not produce more effects than a single
  instance; refer to the specific ability for more information.


Two copies of the triggered ability will mean two damage whenever a sliver attacks.