I did get it working in Prusa Slicer and Orca Slicer. I have included both of those. I have the untitled.obj and untiltled.mtl file. The mtl file references the baked us_flag.png file.
I also included the .blend file. To open the .blend file, I used Blender 5's Layout, UV Editing, and shading tabs. The original PNG image will likely have to be reloaded, rebaked, and exported to obj.
Since the files are relatively large, I uploaded them to Google Drive and am sharing the link here for the public. To correctly display any image file on a print, you first need a high level of triangles, read 2 MILLION+, the more triangles and the smaller they are, the more details you will see in the image in question, but this *WILL* lead to print problems with some areas maybe to small to print and see properly, and you will have to maintain that happy median with printability.
Also, this method of placing an image on a print should work with any image and any print.
Don't bother trying to get Blender to limit to a set number of colors, because once it is Orca-Slicer, you will have to remap the 16 colors to the number of colors you are using. Second point of ref is Prusa-Slicer does *NOT* support importing colors from an obj file. The workaround is to work on it first in Bambu Studio or Orca-slicer, save it as a 3MF file, then open it in Prusa-Slicer and save it, because it will now be in the Prusa format for 3MF.