The output of the step up transformer has a resistance, this, as well as the amount of power going in to the transfromer will limit your output current, however low the apparent "resistance" of the capacitor when initialy uncharged may be. The types of capacitor used in camera flash circuits, usually electrolytic, obviously rated for high voltages, are, I strongly suspect, rated to handle this inrushing current just fine*, I did some projects with camera flash circuit boards many years ago (before I knew very much in terms of electronics) and never noticed anything that looked like a deliberate resistance added between the transformer and the capacitor pins. These electrolytic caps will also have an equivalent series resistance of their own which will further limit how much current they'll draw when initially charging.
*obviously the camera manufactuers assumed relativly infrequent flashing, if you're charging it up and dishacrging again once every few seconds you might have to start worrying about the heat generated in the cap by those regularly repeated periods of higher current during charging.