The palette in 8bit mode is a table that maps values from 0 to 255 to RGB values. You can map lime green or purple or black to 0, 1, etc...
When you work in a higher color mode (16 or 24 bit), 8bit pictures with different palettes can be displayed, because the redering mode supports a wide array of RGB values anyway, and multiple software palettes can be defined.
But in 256 color mode, the hardware only provides a single 256 color palette. If multiple programs modify the palette you're screwed. DOS programs were not meant to work in multitasking environment, so they behave as if they were alone on the machine, and use the palette however they please. There's nothing you can do about it. Windows programs that were supposed to work in multitasking environment in 256 color modes were designed to play nicely with one another (ie, not to mess with the palette). DOSBox is designed to emulate the DOS games properly, and it will try to emulate the palette changes properly, at the expense of the palette of the host if it (the host) runs in 256 color mode.
If you need to run old Windows apps in 256 color mode and DOSBox at the same time, as it has already been suggested, you should leave the host in 24 or 32bit mode and use an emulator or a virtualizer for the old Windows apps. Run Windows 98 in it in 256 color mode, the emulator will take care of simulating the 8bit modes for the programs inside the emulator without messing with the palette of the host. You could also run old DOS programs in the same emulator instead of DOSBox. DOSBox is designed for DOS gaming, and nothing else (although other programs may work as a side effect since you need a comprehensive emulation to reach the compatibility level of DOSBox).
If you explained precisely what you wanted to do (what kind of apps, for DOS, for Windows, which one requires 256 color mode and so on) people here could really help you.
You're far less knowledgeable than you seem to think you are. If you don't help us help you, there's little we can do.
- Why do you use the VGAOnly mode? It's far slower than the normal VGA mode, and is only required for a handful demos.
- Why do you want to play that obscure game while using Win9x programs that require the 256 color mode? Palette cycling was a common technique for animation at the time. But non game programs should not use it much.
Also, this is a message board, not a chat, please use it as such. Capitalization and punctuation are welcome... and don't be afraid to type more than 3 sentences per post.
