L298N Motor shield and 2.8A DC motor - would it fry the shield ?

Using both channels in parallel should be OK. However, you'd be better off using a mosfet h-bridge chip such as Pololu - MC33926 Motor Driver Carrier. It has a much lower voltage drop than the L298N, so it runs much cooler and needs little if any heatsinking.

If you do use the L298N, then you need to provide a supply voltage around 3V to 4V higher than the motor voltage, to allow for the voltage drop in the device.