Game cube has no support for 32bit color. Max bit depth of the framebuffer is 24bit, which can be used as 8:8:8, or 6:6:6:6 if you need destination alpha.
A flicker filter is a a weighted average applied normally applied in the DAC.
In it's simplest form it's a 50/50 filter applied to the even and odd fields (although 3 line filters are more common), what this does is remove high contrast color transitions between the fields, reducing interlaced flicker.
Dreamcast used a 3 line filter, as does GC, Xbox allows the developer to specify the extent of the filter 1, 3, or 5 lines. You can effectively enable one on a PS2 aswell, but for some bizarre reason it isn't the default so a lot of PS2 titles shipped without it.
I would imagine most Xbox games run in 24/32 bit color, 16 bit is pretty ugly and the additional cost is relatively small.