TPS54383 switching regulator components.
I already know my inductance values. I need to know what they should
  be treated for, such as sat and rms values


If the maximum load current is 3A, then you know one thing - the inductor saturation current has to be above this value. 3A flowing in your load is also the average current flowing in the inductor and providing the regulator doesn't enter discontinuous mode, the peak inductor current won't get above 6 amps.


(source: tantosonline.com)  

The above picture shows an inductor in "continuous mode" and also when it enters discontinuous mode.

It's probably a good idea/rule of thumb to make the ripple p-p current about the same as the full-load average current (as an approximation to best practise) and this means the peak inductor current will be 4.5 amps on full load.

For decent efficiency you should choose and inductor that is probably rated twice this value for saturation current. Another rule of thumb.

As for the flyback diode I'd probably choose a 5A device off the top of my head and without going into the details of the device because it's too much to expect!