The BMC rider Kung beat Ukrainian Andrey Grivko in a sprint finish to win stage two of the race for the second time in three years.
Kung and Grivko finished just ahead of the chasing peloton after the pair were the two lone survivors of a four-man breakaway that held a six-minute lead at one point.
Originally due to begin in Champery and cover just over 160km, the stage instead began in Aigle and was reduced to 136.5km with a potentially treacherous descent removed due to chilly temperatures and “light snowfall”.
Felline, who won Tuesday's prologue, stayed eight seconds clear of German Maximilian Schachmann and Jesus Herrada of Spain.
Twice former champion Chris Froome is 36th but only 29 seconds off the lead ahead of Friday's flat 187km stage around Payerne in western Switzerland.
The race ends in Lausanne on Sunday with an 18.3km individual time-trial.