Camera / flash gun tubes are
tiny compared to proper strobe tubes. They are intended for very low duty cycle operation and have very low total discharge life - how many thousand photos is anyone going to take over the life of a consumer flash gun? Professional studio ones are different, they have big tubes.
You would need to drop the discharge capacitor to a tiny fraction of what is typical 330uF used. Maybe 1uF - 10uF depending on frequency. This would drop the energy dissipated in the tube, but also the duration of the flash discharge itself, making it harder to see.
The flash trigger from the camera is usually just a switch contact, but in a lot of cases, this directly connects to the small capacitor that gets discharged into the trigger transformer, so you would need to check out the actual circuitry to trigger it electronically, or just use a 555 timer and a relay.
You haven't given any useful information on what you intend to use the 'strobe' for. Emergency beacon? freezing motion? Disco (
)? Flash frequency / range? The longer light pulse possible with LED strobes (compared to the tiny discharge duration of a flash tube with small capacitor) makes them far better for pinpointing locations.
P.S. Here's an ignition timing strobe that I built donkeys years ago, triggered by the the spark plug HT lead. No it's not mains isolated, but none of them were. Note the difference in strobe tube size against the camera flash tube alongside. I used a 1.8uF film cap btw....