For inductor selection in a buck converter, you usually start by picking how much ripple current you want to allow in the inductor. This is a rule-of-thumb kind of estimation. If you need fast transient response and smallest inductor size you could go as high as 60% ripple current. If you need low output ripple and high efficiency you could go as low as 20%. 40% is usually a good compromise.
(For absolute smallest inductor size at low currents where efficiency isn't paramount you can run the converter in discontinous mode with 100% ripple current.)
Since you need 300mA output current, 40% ripple current is 120mA. Your regulator switches at 52KHz which is a period of 19.23uS. For a buck converter, the duty cycle is Vout/Vin (continuous conduction mode) so your on time is 8uS. During the on time the voltage across the inductor is Vin-Vout or 7V. V=L*dI/dT so your inductor value should be 7V*8uS/120mA = 466uH.
Next you have to make sure the inductor can handle the current without saturating or getting too hot. Check the datasheet for the inductor to make sure you're below those limits. The 330uH inductor you selected has an RMS current maximum of 270mA so it's undersized for this application. The saturation rating is 360mA, and your output current +1/2 ripple current is 360mA, so right on the edge for that rating as well. The inductance would be OK, you would just have higher ripple current than the 466uH calculated above.
Finally, the core loss can be important especially at higher frequencies. This converter operates at a relatively low frequency so most magnetic materials intended for use in SMPS are probably fine. For higher frequencies you have to look at the core loss curves (if available) to see if the part is suitable for use in your design. If no core loss curves are available sometimes there's a frequency range given or an online core loss calculator tool. Otherwise you have to contact the manufacturer for core loss information.