The three should work fine. However, using a simple pot means that all the current will have to go through it. At 350mA, if your battery is 13.8V, and the Vf is 3.42 (see
One simple way around buying a pot like this would be to use a transistor to set the current. One approach is to use a single NPN power transistor (like one in a TO220 case) and use the pot to set the base voltage. This has the disadvantage that the current (and thus the brightness) will vary widely depending on the temperature. However, it may be good enough. Note that the NPN will dissipate that 1.2W as above, so it may need a heatsink, depending on location.
If more precision is required, a 1 ohm resistor between the NPN's emitter and ground can be used to measure the current. This can be used as negative feedback to an opamp, which then is used to control the base of the NPN with its output. By setting the voltage on the positive input, you can control the current with good precision, and the current won't change with temperature. A pot can be used to set the non-inverting input of the opamp. However, even more precision can be obtained by using a temperature compensated voltage reference. This way, your current will no longer be proportional to the input voltage.
However, it just occurred to me that you could use a low voltage TLV431, which uses a 1.2V ref, and a 3.5 ohm sense resistor, like this:
-----------------o-------------- 12V | | | | [led string] [330] | | c\\| | |-b---------o e/| | K | --- o---------R-/ \\ TLV431 | --- [3R5 1W] | A | |
----o------------o--------------- GND
When the current gets above 350mA, the TLV431 will turn on, pulling the base of the NPN lower, thus decreasing the current. This gives you an accurate, temp compensated current source which doesn't depend on the input voltage. It only requires a drop of about 1.5V at 350mA, so it can handle a voltage down to a bit lower than 12V with 3 luxeon emitters in series.