What you seem to show is not a flyback transformer, but what a flyback transformer connects to, a high voltage multiplier diode and capacitor assembly that converts some lower high frequency, high voltage AC voltage from a flyback circuit (about 3kV AC pulses in, 7000 to 12000 DC out). You can test it by feeding putting into the circuit it came from, it it develops the DC HV it is supposed to, then it is ok. If it instead gets hot, arcs over, or seems to otherwise overloads the pulsed transformer circuit that connects to it, then it is not ok.
To test this device, you can create a circuit sometimes known as a Polish Inverter. Create a flyback circuit by borrowing a spark coil from your neighbor's car. Connect one side of the coil to a 1.5V power supply. Connect the other side to a .1uf/600V capacitor to ground. Now from the junction of the capacitor and the coil, connect an alligator clip lead to a large bastard file with sharp horizontal ridges. Now, take a second alligator clip lead and connect one side to ground and the other to a small screwdriver shaft. By rubbing the screwdriver lightly and rapidly along the ridges of the file, you will create a very fast switching circuit that should produce several thousand volt pulses from the spark plug side of the coil connected to the voltage multiplier input pin under test. You should then detect a 9000V to 15000V DC presence at the anode connector output.
Watch out for shocks.