Design of circuit for controlling high power LEDs
This circuit could do what you're looking for. It scraps the bulky relay and replaces it with a very cheap MOSFET transistor.

The central point is your 6 V driving these high-current LEDs with very short flashes from a battery. You haven't given actual timings for the pulse width, though it's likely to have been 5 ms or longer because of your relay switching time. But you might want it to be a lot shorter in the future one.

A 6 V to 2..3 A precision current-limited DC-DC converter could be used to get your LED's current most efficiently. However, that will draw a small standby current and you mentioned this being battery-powered. For the time being, I've shown 1 ohm series resistors from a 3.3 V nearly-3A starting point derived from the LED datasheet. These could be on all the time so are derated by about a third.

I don't know what your plans are but they sound experimental. You might want to build this and get some better data from trial of you application. You could go to a third generation once you have better timings and make more efficient use of LED power than dumping half of it in resistors like this.







simulate this circuit &ndash; Schematic created using CircuitLab

Q1 is a MOSFET with logic-level drive capability. It can conduct 8.3 A of load when driven with 2.5 V min which suits your Arduino General-Purpose Output (GPO). The 8.3 A is plenty for your load, which I've shown as LED1 and LED2.

R1 limits the GPO current flow when charging and discharging the MOSFET's gate capacitance as GPO switches to high or low. R2 ensures that Q1's gate is pulled to an 'off' state when GPO is high impedance. This will be the case on power-up, until the Arduino is out of reset and software has set the I/O pin mode.