How would I go about doing this? I can't seem to find the file folder to load the file into so that I can select it in the SCURK.

You're probably trying to use tilesets for the Windows version of SimCity 2000, but GOG provides the DOS version. They aren't compatible, so make sure the tilesets are for SimCity 2000 DOS version to use them in SCURK.
(DOS tile-sets have a .TIL extention. Windows tile-sets have a .MIF extention.)

Btw, there is a way to convert Win tilesets into DOS tilesets:
With the Windows version of SCURK you can export single buildings to an BMP picture file. Convert it to PCX file format in any picture editing software. Now you can import it in the DOS version of SCURK. Afaik it's the only way to get content from Windows tilesets to DOS tilesets.

I don't think that answers the question. How can I access my filesystem to even load a new tileset. It seems the load file dialog only sees the internals of the dosbox that used by gog to load a DOS game.

You can't see your whole filesystem, because the game runs in an emulated DOS environment (DOSBox).
DOSBox mounts the game's folder (\SimCity 2000 Special Edition) as hard disk C:
Create a subfolder and copy the files there to access them from inside the emulated environment.
(Or mount other parts of your filesystem as further drives in DOSBox, e.g. by editing the \SimCity 2000 Special Edition\*.conf files)