1. Calculating a 4-20mA flow rate from a pressure signal

Yes, the 4-20mA is configurable for flow rate, instead of pressure.  In fact you've done it already.

When you selected "volume flow w/ square root", then the change in mA output reflected the change in output for linear pressure to pressure square rooted to flow rate:

301 Pa on a linear scale of 0-2000 Pa is 6.4mA.

301 Pa on the corresponding square root scale of a normalized 100% flow rate at 2000 Pa is 10.2mA.

Yes, the square root value is larger than the pressure value, because of the relationship of square root values less than 1.000.

The URV is considered the 100% value.   The square root, for flow rate, is NOT calculated on the pressure value, rather the square root is calculated on the "normalized" value of 100%, where the URV = 100% and a normalized 100% = 1.000.

Hence, the square root values are the square root of a value less than 1.000.  For any given value less than 1.000, its square root is a number larger than the value.  

You can prove this by taking your calculator and calculating the square root of any value less than 1.000 and you'll see that the value of the square root any number less than 1.000 is larger than the number itself.

In your case:

The percentage of span for 301Pa is 301/2000Pa = 0.1505 = 15.05% of span

The square root of the normalized 15.05% is the square root of 0.1505 = 0.3880 (38.8% of flow rate)

38.8% of the 4-20mA span is 
38.8% of 16mA = 6.21mA, plus 4.0mA offset = 10.21mA

301pa = 15.05% of the pressure range, which corresponds to 38.8% of the flow range for that primary element.

The overall process concept is that the DCS is configured to interpret/display the flow rate using the square-rooted signal in the appropriate flow range for 0-2000 Pa, whatever that flow range is, according the sizing sheet for the primary flow element.

I cannot recall whether the P320 display can be configured for flow units.

2. Flow rate options
The differences between the various flow rate outputs 
- Volume flow: Hold at 0, square root.
- Volume flow: Linear, square root.
- Volume flow: 2 step linear, square root 
are explained on two pages in the 2025 edition of P320 HART manual, with graphs in section 9.2.4.5 "Volume and mass flow measurements".

Essentially, the differences are for low-flow cut-off at the lower end of the pressure scale, where it well known that the accuracy of DP flow measurement accuracy drops off drastically at low flow rates/low pressure measurements.

See the Siemens Youtube video, "Setting up the SITRANS P320 for Flow Measurement"

for configuring a P320 for flow measurement with a DP primary flow element.

https://www.youtube.com/watch?v=WLZukTWQBOA

Setting up the display to show flow units starts at 5:55