Sure it's for lower power application, but for testing the theory from the book, I think that's enough. So, I'm building right now a low power battery charger for 4V lead acid battery that has an output of 4.5V and 500mA, and utilises an isolated flyback topology. That's why I need to design a CC/CV feedback for the chip, to ensure the battery doesn't draw too much current.
Well, if you just start with a current mode flyback controller, the output current will be limited (if crudely) simply by virtue that the controller cannot deliver any more current than its maximum rating. The crudeness occurs because, as the output voltage decreases, the duty cycle increases, so the output current increases. If the input waveform remained constant, it would actually be a constant power relationship. But that doesn't happen, so it's kind of something inbetween.
Ah, I forgot that LNK364 is one that's self-powered without an aux winding. This suggests it'll operate down to low output voltages... but, it also has a "fault detect", which they don't happen to say how it's detecting a fault condition.
So LNK364 won't actually go to low output voltages while current limiting.
As for the load: are you expecting to charge batteries that are completely flat (~0V)? Maybe it's an advantage, that the output current will be very low (because of the low duty cycle of the fault counter) until the controller leaves fault mode. Gentle charging. Maybe not necessary for lead acid.
How do you power up SMPS controller ICs that have much lower voltage that the line voltage (110V/220V)? Is a voltage divider a good solution? Or should an auxiliary power, maybe using the LNK chip again, be used?
If not for the internal fault circuit, the LNK alone would be fine -- it has a "voltage divider" sort of supply (well, an active one, a regulator, but it's burning a lot of power in the process, as a resistor does), and runs from that, all the time.
A traditional one like UC3842 needs an external supply. It could be, yes, another LNK chip, or an off the shelf module (saves you the trouble of specifying another transformer and building the circuitry), or a buck regulator like one of these,
https://www.monolithicpower.com/DesktopModules/DocumentManage/API/Document/GetDocument?id=5Is limiting inrush current with NTC thermistor a really good solution? Is there better solution without using NTC?
I'm not very worried about inrush on small things. Tossing an NTC on there is a cheap way to obtain it. Small supplies (like most LNK applications) don't even need an NTC, a regular resistor can be used (without costing much efficiency). The resistor can also be a fusible type, eliminating the fuse component too.
If you're designing for CE market, you'll want to make sure all the EMC (including inrush, dips and swells, EMI...) are in order.
You said "...to eliminate the primary side supply...", does this mean the controller is put into the secondary side? How do you power the controller? Because you see, it's like a chicken and an egg problem. The secondary side gets its power from driving the primary side, but to have the controller to drive the primary side switches, you need to have power from the secondary side. 
You still need some initial power source, but as above, it can be a small PSU module, or a LNK circuit or whatever.

If you need controls on both primary and secondary side, it's more reasonable to eliminate the primary side controls (using a gate drive transformer to pass signals to the primary side switch(es)), than to eliminate the secondary side controls (because you still need some kind of power source to sense the output voltage and current, all the way down to zero output).
Tim