I don't think you'll be able to find small variable resistors with such low resistance.
To have a variable-current LED driver running from a pot, there's typically a fixed current-sense resistor, and a pot is used to modify the voltage going to the current-sense input of the driver chip.
One way is to have the fixed sense resistor as usual, but to add another fixed resistor (maybe a few kilohms) between it and the driver chip, and to connect a pot of rather higher resistance between the driver sense input and the positive supply.
The pot is chosen so at maximum resistance it is barely influencing things, and the drive current is at the level set by the fixed current-sense resistor.
As the pot is operated and its resistance lowered, it adds to the voltage coming from the current sense resistor, effectively 'fooling' the driver chip into thinking the drive current is higher than it really is, causing the chip to lower the actual drive current.
Some datasheets for driver chips might include example circuits.
