I developed Grafx2 for the longest time on my Windows 98 computer, with an AGP x1 videocard. If v2.4.2035 doesn't start, it means I made a mistake when I compiled it, just tell me and I'll rebuild it.
The SDL2 version doesn't work. The advantage is hardware acceleration and UI no longer depends on image palette. The downside is that I'm not sure it will be completed ever, SDL2 is so buggy compared to SDL1...
Edit: Just checked, Grafx2 2.4 works fine.
Other freeware painting programs which I can confirm work on win98 :
Pixelformer, rather for high-color stuff, but very easy to use and I love how you can draw/edit the alpha channel directly
EvilPixie, very cute
Pencil 0.4.4 (not pixel art, animation)
GraphicsGale (demo I think, 1.93.19)
Let me know if you need to track specific versions.