Although this has been answered on my private discord, i thought i should address it here too in case someone comes across with the same question:
-For NESmaker users, i think the easiest method is using the .chr import feature instead
-Right now, if not wanting to do that, you can define an emulator palette (192 bytes) as black, red, green, blue on the 4 brightness tiers and put it as nes.pal in NEXXT:s home folder. Then, go to palettes > system palette > external [...]. Then you can export that as BMP.
-A system palette browser is on the roadmap. It's a medium-priority feature. (Examples of higher priority features is a metatile tool & a working metasprite animator).