Saturated solution of KNO₃ is used to construct salt bridge because

The main function of salt bridge is to complete the circuit by facilitating the flow of ions through it. 

Negative ions flow to the anode and positive ions flow to the cathode through the salt bridge. In this way, the charge balance is maintained and the cell keeps on functioning. The criterion for the selection of salt in the salt bridge is that the ionic mobilities of cation and anion of the respective salt are nearly same.

KNO₃ is used in salt bridge because the velocities of cations and anions in KNO₃ is nearly the same.