Safe assumption for AA and C battery current draw
LED candles are often a small microcontroller of some sort (to create a flicker effect) and one or more LEDs. Aside from on (flickering) and off, what other cycles or modes do your candles exhibit?

You size the power supply based on the maximum current that the load will draw at a given moment. Your question implies you might think you need to measure the average current drawn over some period of time, but this would be more for calculating power consumption, not current draw. (See Olin's Q&amp;A about calculating power supply requirements.)

If you measure current when the candle is operating at maximum brightness (or whatever constitutes its maximum setting), this will give you the amount of current required, and can be summed with the other devices to inform your power supply choice. For example, if you measured 100mA for the highest-draw LED candle, you could likely assume that 500mA is sufficient to operate them all. I would always recommend adding some overhead for things like inrush current, etc. Remember, the load determines the current draw, not the capability of the power supply. Therefore, having a power supply rated for more current just means it can handle more than may be needed.

A 3V 1.67A power supply can be found for less than $6 (example at All Electronics). This is just based on a guess -- you'll need to measure the candles to be sure. Keep in mind you could just purchase something like a Meanwell LRS-50-3.3 for less than $15 USD (example at Mouser), and have 10 amperes available for whatever 3V applications you want. (That supply is 3.3V but adjustable from 2.97 to 3.6V.) It's extremely doubtful your candles require anywhere near that much, so for the price, the problem is solved without having to spend too much time measuring and calculating the requirements more precisely.