Flux walking, also known as flux stair casing, is the successive accumulation of flux in a magnetic core ultimately leading to its saturation. In any circuit involving magnetic elements operating in steady state, the net (volt x time) product applied to the core must be exactly zero. If you have more than one piece of magnetics, the volt-second balance must hold for every one of them individually. Voltage polarity should be accounted for and summed over one switching cycle. Even the slightest unbalance will result in a bit of residual flux that will continue to pile up in each cycle, hence the staircase analogy.
There are several ways to avoid it, basic principle is to make sure that volt-seconds applied in one polarity are exactly equal to volt-seconds applied in the opposite direction in each switching cycle. AC coupled capacitor which manipulates the voltages to achieve balance, or current mode control which manipulates time to achieve the balance are two examples.
The peak current mode control (PCM) is the simplest way to prevent the transformer of saturation. FB PS ZVS control usually applies PCM with the primary current sense. The only trap here is that the converter must operate always with some margin of the duty cycle. If in some transitional state it comes to the maximum available duty cycle the feedback loop is open and obviously the magnetizing current is off the control. It can be improved by the implementation of the secondary current sense (with preservation of the primary current sense). There are few methods of dealing with double current sense. It should be obvious that from the both currents, the magnetizing current can be derived.