If it's like my computer screen, pretty darn flat.
The same applies to the EIZO monitors that Camera Electronic sells - wonderfully professional display devices that are far more accurate that the eyes that peer into them. Even if you are off, the EIZO's are on.
But what about the results from your newly printed analogue image? The wonderfully retro art that the new film shooter has been able to produce in only a week? What does it look like?
Well, if the neg or slide went into a professional lab and came out as a RA-4 or inkjet print - pretty darn flat as well. Ditto if the photographer did it at home through the scan-compute-inkjet route. Prints from the output tray of my Epson R3000 printer on Epson or Ilford papers come out nearly as flat as the paper that went in the feed slot. The addition of ink makes for a little buckling, but this gasses off and dries out and the final prints are dead flat again.
Note that I always store my printing paper in its original package, flat, and in dry, cool conditions. Standard inkjet material is forgiving, but A4 decal printing sheets can die unborn if they encounter heat or humidity.
Now back to the home-made print. If the darkroom printer has used Ilford resin-coated paper the end result will also be flat. With a final squeegee and dry, it is ready for mounting or storage.
If the printer has decided to use fibre-based paper - the non-coated type - for artistic reasons, they have taken on a much curlier problem - their final print will have a mind of its own and will resist most efforts to make it lie down and behave.
The culprit in this is the photographic emulsion on the top and the fibres of the paper under it. The top will take the image but the bottom swells in response to the developer, the fiver and the wash water. Then the top contracts as the print dries and curls or buckles it up. You can flatten some prints later, and some prints can flatten you. There are a number of liquid solutions that reduce this curl and a number of mechanical processes that can combat it, but totally flat fibre prints are only possible with commercial drum driers or carefully-maintained ferro-type plates.
Do not expect a rapid workflow with fibre-based enlargements. But embrace this fact, and commit only those images to this demanding technique as would be artistically justified.
How do you achieve ultimate flatness? Or flatnessosity, if you want to use the technical term - mount your fibre-based print on a board. With mounting tissue. And a giant hot press. If you want perfection you must be prepared to scorch yourself for it.