Well as mentioned before, you'll first need to solder a bigger ROM chip in place of the one that's already there. That's the hard part. These are surface-mounted chips and you need special tools and the technical expertise to do it properly. This has been a common problem with flashing NVIDIA cards since the GTX 285, unfortunately. The Rominator (I think he still hangs around at netkas) knows how, but he's based in LA.
The flashing itself is the easy part. But you have to do this in Windows because NVIDIA cards get flashed with a tool called nvflash and a Mac version of the tool does not exist.
If you're looking to build a Resolve system (and presumably make money with it), you'll have to ask yourself if the DIY approach is even worth considering. A paid job or two would easily make up for the difference in price. Also, consider used Mac GTX 285s. These work very well with Resolve, too.