Where on the logic board is the flash memory that comprises the OS on the iPhone 3GS?

Staring at the guts of my dated phone, I was curious how feasibly I might remove the logic board, swap it with another, and resume normal operations.

As such, I've been hunting for pics detailed iPhone innards but I've found nothing more than an obscure forum post or the iFixit teardown.

Is swapping logic boards possible? Will it impact the entire phone?

All of your data is stored on the flash memory, which is one of the chips soldered on to the logic board. It's not really possible to swap the memory to a different board (perhaps if you had advanced electronics skills, but I wouldn't like the chances of success).

If there's a problem with your logic board, you can replace it with a new one, as detailed in that iFixit link. Assuming everything goes to plan, and you have no other issues with the phone, it will effectively be a new iPhone. If you have a backup of your old one, you should be able to restore your data during the set up process.