I will never work. The difference between a flash (Xenon) tube and LED is that the tube will not conduct until maybe 600 - 700 volts is applied directly across it. An LED in comparison will conduct at only 3 - 4 volts. The tube is run at a lower voltage, typically 300V and will not flash until a high voltage pulse is applied at the trigger electrode. This does two things, being closer to the common end of the tube it has a much shorter distance (= needs lower voltage) to ionize through and it when ionized the cascade effect is to allow the remainder of the tube to conduct. When the voltage across it has fallen enough, the tube extinguishes and the inverter starts to recharge the reservoir for the next flash. The second transformer, used to generate the trigger is usually just a tapped inductor, used as an auto-transformer.
To make an LED work, you need to wire it in series with the trigger switch but ensure a lower voltage is always present to power it. Unfortunately, the available 1.5V is not enough so you still need some kind of inverter to give it a boost. You need to change high voltage/low current into low voltage/high current. The existing trigger electrode and transformer become redundant, the last thing you want connected to an LED is a spike of several hundred volts!
Brian.