Why is there a huge difference between Is2(peak) and Is2(rms) in flyback converter?
As you might already know the primary winding (actually, its magnetic field) stores energy during the primary switch remains on:
$$
E=0.5\ L_p\ I_{p-pk}^2
$$
And, this energy will be transferred (partially or completely, depending on the operations mode -- DCM or CCM) to secondary/secondaries once the primary switch opens.

IS2(peak) = Ip(peak) x Np/Ns2

Technically the formula assumes that all the energy is transferred to this winding (i.e. Vcc winding). But this is not what actually happens because the Vcc winding does not consume all the energy that is stored by the primary. Its requirement is about 1% of the total. That's why it's almost always neglected. But,

Is1(peak) = Ip(peak) x Np/Ns1

This is correct. Because 99% of the total energy is consumed by this main secondary. Check the power ratings of the secondaries: 18 × 0.02 = 360mW for Vcc, and 24V × 1.5 = 36W for main secondary.
Remember that we almost always neglect the power consumption of the Vcc winding. Because it really does not make much difference: ~36.4W against 36W.
PS: I personally recommend you to study switching power supplies from these two books: Switching Power Supply Design from A. Pressman, and Switchmode Power Supply Handbook from K. Billings.