Triggering an LED Flash
I like to use solid state relays for this sort of thing.  They provide isolation (often for your safety but in this case to avoid frying your kit).  They're faster and use less current than a mechanical relay, and simple to integrate.

An Arduino can apparently deliver 40&nbsp;mA on a GPIO pin.  This arbitrarily selected DC SSR wants &le;30&nbsp;mA and drops around 1.5V so will only need a simple resistor to drive it off a GPIO pin. It can switch 10&nbsp;A if the two internal MOSFETs are connected in parallel, and the through-hole version can be assembled on stripboard or dead bug style (glued down on its back with its legs sticking up.  The current capability is more than enough, because we don't know how much that lamp draws.

As it has a dimmer as well, there's probably an LED driver chip in there, but I assume from my experience of hacking LED lights that the on/off switch is connected to the power supply line (in contrast to bike lights, where it's often an input to the LED driver).

When it comes to making the connections inside the lamp, that depends on exactly what you want to do.  Your options are:


Replace the on-off switch with the SSR
Wire the SSR in parallel with the existing on-off switch (this allows you to turn the light on without the Arduino)
Wire the SSR in series with the switch (this allows you to force the lamp off).


The biggest problem I see is if my assumption above is wrong, and you have an on-off switch that connects to a logic pin on an LED driver chip.  The only way to find this out is to open up the lamp and trace the circuit.  You can usually replace such a switch with an opto-isolator, but the details will depend on the existing circuit.