Thumbing with both hands
Under IV: How to strike in the official rules


  
  Any hand may be used in play.
  


Hand in this case is singular. This is somewhat clarified further down...


  
  The elbow of the playing “hand” shall not come within the playing surface nor shall extend beyond the imaginary lines of the arrows. The “hand” may, however, cross the arrow.
  


This indicates that there should only be one hand in use.

The rules also indicate what the other hand could be used for


  
  While making a stroke, taking support of the Stool or Chair, Stand or Table of the C/B or keeping the legs on the rim of the stand or table by the player is not permissible. However, hands may rest on his body and legs or on the rim of the stool or chair on which he sits.
  


Furthermore, if you wanted to make an analogy with cue-sports, there is almost always a rule against double stroking or push strokes, as the concept of a "stroke" is one single instantaneous point of contact. Carrom's definition gives some more leeway because we're using fingers instead of cue sticks, but the concept is still the same. Using two fingers undoubtedly results in striking the striker twice.