Perhaps micros() would be better for this. Didn't you say you are going to have LEDs counting in 0.1ms aka 100uS timing? I'd have another row of LEDs counting at 10us intervals.
You need to be precise in your questions, precise in reading follow-up questions and answers, and precise in your answers.
I'm unclear about how the LEDs counting is going to tell you the time between the shutter opening and the flash going off. Or at least how a photo of the LEDs helps you.
So the button is pressed, you can access that signal.
Some unknown amount of time passes before the shutter opens. I guess you need this time.
Some unknown amount of time passes after the shutter opens, before the flash goes off. You need this time.
How about this:
LEDs all lit, every one. Just bright enough to show in the photo.
Send a button press signal from the Arduino, at the same time the Arduino starts turning LEDs off. It is NOT counting down, it is counting up but the count is in dark LEDs.
Some milliseconds later, the shutter opens. All the LEDs that are dark when the shutter opens show as dark. Stay with me... the LEDs that go out while the shutter is open merely appear dimmer, so the image shows an accurate time from button press to shutter opening.
Some (probably microseconds) time later, the flash goes off. A fast photodiode sensor or an electrical pulse detector signals the Arduino and it stops the LEDs from counting.
Now look at the time represented by dark LEDs in the photo and the dark LEDs on the display as it is now. The difference is the time between shutter opening and flash going off.
Why not have the LEDs simply start out dark and light up as it counts up? Shutter opens, all lit LEDs show. However, the shutter is open for 0.25ms so more LEDs will light up. They will look gradually darker the later they light after the shutter opens, but an LED that lights right after the shutter opens is going to be nearly indistinguishable from one that lit before the shutter opened.
I'm not sure counting by decades is going to work. Say it just counts from 1 to 2ms as the shutter opens. Well, then the 0.1ms LEDs all change state together and continue counting up. During a long 0.25ms shutter time, that is going to be ambiguous, no matter how you slice it.
It might be better to line up 50 LEDs to count (again, light to dark) by 0.05ms each. That's 2.5ms and your shutter time is only 0.25ms, should be long enough. The micros() timer has a granularity of 4us. Use it to time the LEDs.
If there is a long time from button press to shutter opening, figure out how constant the time is from button press to shutter opening, and delay counting a fixed time to put the shutter opening within that window of time.