Yes, it is that easy. I built a couple when I was a teenager using random cores (different torroids and ferrite rods) and they worked well (i.e. they charged a cap quickly). ...For preliminary testing, you can just wrap some wire around a torroid, or run a simulation or two.
The core, and the number of turns will determine the inductance, as well as saturation current. With a feedback winding for a self oscillating converter/charger it'll run at the frequency determined by this inductance, voltage input, and voltage output. Whilst it'll probably work with a toroid, efficiency, current consumption (and therefore charge time) will vary greatly with core material and windings. Good for trial and error and for a prototype, but a hassle to have any sort of control over battery life, charge time etc.. Almost all of these transformers will have a 'gap' in the core where it can store more energy. So if you roll your own, you'll need to buy pre-gapped cores.
Because the voltage across the primary coil is proportional to that across the secondary coil, it's easy to sense the output voltage without a dedicated supplementary feedback circuit. IIRC they do use a cycle-by-cycle current-limit, but this is common for many SMPS controller ICs.
I meant feedback windings that are used in single transistor self-oscillating flyback converters, not for measuring capacitor voltage, but to determine what the field is doing in the transformer. But you're right, you can sense the caps output voltage via the primary peak voltage.
To the OP:
Its true, they are essentially boost converters with added circuitry specifically designed for flybacks (isolated boost converter) to charge capacitors. Unlike a boost converter though, it doesn't regulate output voltage quickly, as the output cap is expected to be large, instead it just stops charging when a preset output voltage is achieved. In simpler circuits like the ones from that store, and in most camera's, because the charger is self oscillating, its remarkably simple, and its efficiency, power consumption (charge time) is determined by the transformer characteristics rather than circuit control.
I've found with my own flash cricuits/cap chargers that its either a simple and cheap circuit, with critical parts like the transformer - fixed characteristics, but does the job well. Or, one that uses clever control, with many more parts, but relaxes the constraints put on the transformer/inductor design. Obviously for mass production, simple/cheap is better so I think you're going down the right road here. If of course you want to make it very efficient, small, or have some digital control over it, then IC's specifically designed for the task would be handy. For the most part though, anyone using a flash just wants to trigger it, and then expects to wait until its charged without having a countdown or charge monitor or anything, simple is better.
That component you found for charging 80uF, the size of the capacitor doesn't matter to the charger - these things just pump current into caps, so as ronv said, it'll just take longer to charge. Its not *quite* as simple as 'double the capacitance = double the charge time' because as it charges, it takes more current. But the charger doesn't care. If you want faster charging using an IC driver, you will need to increase the current limit, or increase the input voltage.
Sorry for the long posts, years ago I was intrigued by these little converters found in disposable camera's and spent far too long working out what was happening and building my own :/ (wasted youth eh?)
Just remembered I had this on my PC, great little app note!
https://www.electro-tech-online.com/custompdfs/2012/11/dn25.pdf