I followed this description: http://worms2d.info/Palette_file

SetDirectory[NotebookDirectory[]];
ClearAll[ExportPal]
ExportPal[fnout_String,colors_List]:=Module[{colorout,length,str},colorout=Select[colors,ColorQ];
    If[Length[colorout]>0,
        colorout=List@@@(ColorConvert[#,"RGB"]&/@colorout);
        colorout=Take[#,3]&/@colorout; (* remove alpha channel if present *)
        colorout=Append[0]/@Round[255 colorout];
        length=4+4+4+4+2+2+4Length[colors];
        str=OpenWrite[fnout,BinaryFormat->True];
        BinaryWrite[str,"RIFF"];
        BinaryWrite[str,length,"Integer32"];
        BinaryWrite[str,"PAL "];
        BinaryWrite[str,"data"];
        BinaryWrite[str,4Length[colors]+4,"Integer32"];
        BinaryWrite[str,16^^0300,"Integer16"];
        BinaryWrite[str,Length[colors],"Integer16"];
        BinaryWrite[str,Join@@colorout,"Byte"];
        Close[str]
    ,
        Print["plz check z colors, something wrong! kthxbye!"];
        Abort[]
    ]
]
ExportPal["out.pal",{RGBColor[0.5,0.1,0.8,0.1],Blue,Green,LABColor[0.33,-0.48,-0.54]}]

Unfortunately I don't have any software to test the pal file... so let me know if it works...

I made a small update to the code, in case you give an rgb color with alpha-channel.

May I ask why do you need that if you can plot most of things in Mathematica directly?