At 30 Amps, that's a 0.15V drop across the resistor, and 9 Watts dissipated. Not many surface mount shunt resistors go above 5W. I'd go to 0.0025 Ohm or less.
There are high side current shunt amplifiers that have 0.1% accuracy amplification stages that are designed to use the really small shunt resistor values to lower energy loss and still provide enough accuracy. Pay attention to the maximum mV the input stages can accept. The one I plan on using only accepts up to 83mV shunt resistor voltage. Using a 0.001 Ohm shunt resistor with it, I get a usable 30 Amps monitoring capacity. I'm putting an input filter and protection circuit between the shunt and current shunt monitoring chip. I loose some accuracy and range of measurement, but I'm still better than 1% accuracy before calibration. It also means I can accidentally short my monitored rail without worrying about blowing the input stage of the amplifier.
Could you clarify how you got that number? The formula I'm using is just I2R, which gives 4.5W of power dissipated, not 9. I agree that I won't find an SMD device for 9W easily.
I have low-side amplifiers in my setup (DRV8323SRTAR), those have a max 40V/V gain but I'm still figuring out the equations for the resistor value.
One of the issues is that I'm still trying to get the motor supplier to give me the stall current of the motors. If he doesn't, I might have to wait until they arrive to measure it myself, so at the moment the 30A is an approximation. If I size the electronics to just barely accommodate 30A and it turns out to be 35, I'd not be in good shape.
Oops, looks like an error in the spreadsheet I wrote in the middle of the night a few weeks ago. Kinda interesting that I had worst case Watts calculated correctly, and nominal Watts wrong. After fixing the inputs, I also get 4.5 Watts now. Still, there should be more than a half Watt of headroom. That resistor will be heating up a lot, and that will effect accuracy.
Now, for over current for a motor, high accuracy isn't as much of a need. A few % off is OK. Is a 4 terminal resistor even needed? Yeah, if you go with a 2 terminal do the traces for the kelvin sensing like the AMD app note suggests to retain as much accuracy as possible, but do you need sub 1% accuracy, or even sub 2%? I see +/-5% talked about for some control resistors in the spec sheet. Also most motor control circuits are usually cost sensitive, not high accuracy sensitive. If they need accuracy, they use some form of feedback loop.
BTW: A 0.005 Ohm 5W 0.1% 4 terminal surface mount shunt resistor is available at DigiKey. Vishay Foil Resistors part number Y14740R00500B0W. Also looks like you can get a 1% 4 terminal surface mount shunt resistor for a fraction of the cost.
On kelvin sensing for 2 terminal resistors. Not all 2 terminal sense resistors are packaged so the terminals are under the resistor element like the one the AMD app note used. Some have them flanking the resistor to each side, see Stackpole Electronics Inc. part number CSSH2728FT5L00. From reading between the lines, they would be best to have the sense wires to come out the inside sides of the pads. That would allow for no vias in the kelvin sense lines.