Estimate safe ESC curerent for 4108 600kv motors?

Myriad factors contribute to the current draw of a drone motor including supply voltage, motor kV, the propeller geometry (i.e. diameter, number of blades, pitch), ambient atmospheric conditions, etc.

One can make educated guesses and estimations of the current a motor will draw under known conditions, but the best and most accurate/reliable method is to test the desired setup and measure the current draw under the expected operating conditions. If you can, you should try this by assembling the motor and propeller on a thrust stand and powering the motor while measuring the current draw with an ammeter.

---

From the Banggood listing linked to in the OP:

The motor of interest here is the 600 kV variant, which appears to be rated for up to 6S voltage, but power draw is only displayed for 4S voltages. If we take the rough assumption that the motor's current draw will increase linearly with the supply voltage (also assuming all other conditions are unchanged), then we can estimate the current draw for the listed propellers running on a 6S batery:

$$begin{align} text{New Current Draw} &= frac{text{New Voltage}}{text{Old Voltage}} times text{Old Current Draw} \ &= frac{6s}{4s} times text{Old Current Draw} \ &= 1.5 times text{Old Current Draw} end{align} $$

• APC1238 (12" prop, 3.8" pitch): 25.8 A
• APC1447 (14" prop, 4.7" pitch): 33.75 A
• 1555CF (15" prop, 5.5" pitch): 34.5 A

NOTE: These are incredibly rough estimates. I highly encourage experimentally determining the true current draw of your intended setup.

NOTE: These calculations will be irrelevant if you're not using the same propellers as the ones cited in the experimental performance data.

As @Kralc mentions in his answer, you should add a roughly 20% safety margin on top of the expected current draw when spec'ing out an ESC to account for any unforeseen situations.