Power supply and circuit breaker for a bursty device
You are in a tight spot here with one supply and two differnt load requirements. Your obvious brute force solution would be a 23 A supply. If that's not a solution for you, I can see three ways forward, each with their own pros and cons.

Constant current limited power supply:







simulate this circuit &ndash; Schematic created using CircuitLab
With 200 mF and 5 A available for the strobe, you will limit the drop to 20 V during a 50 ms 15 A burst. If this is ok with your other loads, you are good to go. I'm suspecting this will be an expensive and bulky solution.

Normal 24 V power supply plus RC filter:







simulate this circuit
If you can spare 4 A peak and live with ~20 V average on your strobe, this will work with a normal constant voltage power supply. A bit wasteful though.

CVCC supply with individual diodes:







simulate this circuit

Both other loads and stobe will see slightly lower voltage than 24 V during charging but if you can tweak your supply to slightly above 24 V to give you some headroom plus compensate for the diode drops, this might be ok.