You are right to be confused.
What is the meaning of "flyback diode"?
For a "flyback" diode in parallel with an inductance, and meant to dissipate inductor energy when current through the inductor is interrupted, larger Vf for fixed current dissipates this energy more quickly. (By the way, you should not depend only on maximum current rating to judge if the diode is a good fit. You MAY ALSO have to calculate power dissipated in the junction, the junction temperature rise over ambient, know the max ambient temperature, and ensure the max junction temperature is less than the data sheet. If the frequency of operation gets high enough, the diode will burn out even if the current is less than the maximum peak current on the data sheet.)
Now, for a "flyback diode" used as a diode in a "flyback" circuit which boosts voltage, the efficiency of the circuit will be higher for a diode with low Vf at a fixed current. Reverse recovery figures prominently into the efficiency calculation so reverse recovery is important too.
So you can see there is some confusion because there are two different answers.
In general, it is much better to discuss circuit questions with a schematic. Otherwise, improper generalizations are inevitable.