You need a LOT MORE than just wires to carry heat (unless you're talking transmission power line sized wiring...).
The tech section for maxFlex on my website is pretty clear about working out how many watts of heat will be generated within maxFlex based on your load and drive current.
That heat MUST BE REMOVED and that is why there is a thermal pad on maxFlex. You need to thermally epoxy or solder a heatsink/tab to that spot.
The board will get hot rapidly if you are driving 1W or more. Just get a resistor and run it at 1W or more and see if you go ouch when you touch it
There is no free lunch when it comes to driving LEDs at high power. If you have 10W going to the LEDs, even at 90% efficiency that means you'll have 1W of heat being generated by the driver - you do need to get rid of that or the driver will cook/shutdown/be damaged.
Some of you "nuts" are talking about 5 LEDs or 6 LEDs at 1A or more - now we have 20W+ to the LEDs and 2W+ being generated in the driver. 2W will cook the driver very quickly (within a minute). Oh - unlike meat, cooking a driver is not a good idea
There is a reason I put that thermal interface area on maxFlex - it is to be USED. It is the BEST place to get the heat off the board because it is thermally connected by 9 microvias to the backside of the thermal pad of the switcher IC (on the other side of the PCB). That area is THE area that will get hot fast and needs to be connected to a heatsink/tab etc.
Anyhow, hopefully this answers some of your questions...
cheers,
george.