Lets say that I'm using Victoria Jaton (2, Flip Victoria Jaton -> Weapon cards in your hand are instant this turn.) And some one plays an ability that I want to do something about before it enters play, fire ball or what ever.

would it be legal to to flip Victoria Jaton in responce to that ability, play Silent Fang (2, Destroy Silent Fang -> interrupt target ability card) and then use the ability of Silent Fang?

Once people are done adding to the chain does the whole chain need to fully resolve before new effects can be added to it?

You would be allowed to do that. Everything you need to know about this is on page 26 of the rulebook. It is a legal move by all means.