All of these settings can be changed when exporting your files from light room. To check this, open lightroom, look at any picture, and choose File > Export. Under file settings, choose TIFF, and look at the options.
Tiff: That's the file type. Seeing as you have a 5d3, your images will come out of the camera either as RAW (.CR2) or as JPG (.jpg). They are wanting TIFF files (.tif or .tiff).
Colour Space: RGB : This is basically a formula for how colors look. Since you're exporting to TIFF, you can just choose Adobe Rgb (1998) and kill two birds with one stone.
Colour Ratio: not a clue. They are likely referring to the bit depth. You can set that to 8, and probably keep them happy.
Since this seems like the gallery's specifications rather than your friends, I think you'll be fine. Basically, you'll want even lighting across the painting. If it were me, also having never shot this type of photography, I'd look for very diffused lighting, avoid any highlights anywhere on the work, and shoot it at f/5.6-f/8. Hope this helps.
*disclaimer* These are the thoughts of someone that has never shot this kind of photography. If someone has shot this type before, feel free to correct me.
Now... As a further note about the flash, when I think of flash, I think about it's purpose as "accenting the depth of a scene". Since your scene is a painting, you don't want to add any depth, but just show what's there. You want the scene to be pretty "flat" because you're reproducing something that is in two dimensions. Diffuse lighting will help to keep shadows from adding depth (darkness) to parts of the painting that aren't actually there when viewed. The biggest challenge you're likely to face is making sure that ambient lights aren't making hot-spots on your image. Flagging or diffusing those, and keeping the environment very controlled will likely be your best bet to keeping everyone happy.