There are a couple of ways. All involve having either a digital multimeter (DMM) with DC current settings, or a power supply with a current reading. If you don't have a DMM, you can get one as cheap as $4 at Harbor Freight. At that price its only a little better than a toy, but it should get you close enough for what you need.
Unfortunately, for all of these, you need a working LED, so you'll need to either fix yours or get a similar one. If the currents are up above a hundred milliAmps, you'll need the LED to be on an MCPCB, which you probably want anyway. If above a few hundred milliAmps, you'll need that MCPCB to be mounted on a heatsink. During the testing you'll need to pay attention to the current and the LED temperature to avoid frying the LED. If you start low and increase slowly, you can keep everything safe. If not... well, I have fried a $50 LED in about the time it takes to blink. It literally looked like a camera strobe.
The way to stay safe is: start with the supply voltage below the LED voltage (or within the known safe voltages for your setup), increase slowly, monitor LED temps (I use a finger for this, no high-tech).
1. Connect the meter in series between the back of the batteries and the spring on the tailcap. Obviously you have to remove the tailcap for this, and somehow make all the connections. This measures the battery current. It's also often referred to as the tailcap current, as it is the current that passes through the switching mechanism in the tailcap, which can easily be the limiting factor in a design. In this light the LED current would be the same as or a bit higher than the tailcap current.
2. Place a power supply in place of the batteries. Same connection issues as above. Start with the voltage around 3V. Increase the voltage slowly to 4.5 volts. Stop if the current reaches 3A (max rating for the XML). If the current stops going up, you can stop there. This also measures the battery/tailcap current. But this test can also tell you what type of driver you have. If the current stops going up and remains constant, you have a linear driver. If the current actually starts coming down as the voltage goes up, you have a buck type switching driver. In either case, the peak current is probably very close to the LED current.
3. Since you have already unsoldered the LED board, you probably won't mind actually putting the meter in series with the LED. This would measure the actual LED current. If you use batteries, you get the current at one particular battery voltage. Doing the test with the power supply instead can give you a lot more information. Or you can run the batteries down and get the same data. It just takes longer.
Keep in mind that a DMM in current mode will introduce an additional resistance to the circuit. This can affect the behavior of the circuit. In some cases this is trivial, but given the high currents and low voltages we're talking about, it can be quite significant. We can talk more about this later if it comes up.