Hi Vishal,
DOUT/DRDY is tri-state when CS is high. The DRDY pin is an active output pin at all times. You cannot tie two active output pins together or they will fight against one another (contention).
As you have mentioned, you can SYNC the devices together and use just one DRDY pin or the DOUT/DRDY. To keep the devices in SYNC they will need to use the same clock source. This can be done with an external oscillator connected to each of the devices CLK input pin. The easiest way to start conversion is to use the START pin for synchronization.
Best regards,
Bob B