For a flyback converter you *NEED* that inductive spike. If you damp it out with an anti/parallel diode, you are limiting the dI/dt which is directly proportional to the rate of change of flux and thus the voltage induced in the secondary.
The classic diode snubber circuit for flybacks has a fast diode in series with a parallelled resistor and capacitor D-(R|C). The resistor is chosen to discharge the capacitor sufficiently between pulses to keep the voltage below the max Vcbo of the transistor (assuming a low impedance base drive, otherwise Vceo), and the capacitor is chosen as a compromise between size/cost, minimising the voltage swin during a pulse so it can operate closer to max Vcbo, and the startup load due to the flyback having to charge the snubber cap to its intended voltage before the secondary output will reach its design value.
For initial experimentation, replace the resistor with a series string of a much smaller resistor that will drop approx 10% of the max Vcbo if the maximum inductor current is passed through it and one or more reverse biassed Zener diodes, to make up the bulk of the snubber discharge voltage drop, of 70% of max Vcbo. That configuration although a lot more expensive is far more forgiving if the back-EMF spike is larger than expected, or the load on the secondary is varying and once the mean discharge current has been determined, you *may* then be able to replace it with a simple D-(R|C) snubber.