Looking at the code, it seems the problem arises in LinearMix procedure when transition is not tsPlain.
There I was yesterday too

I wonder if the black pixels are in fact transparent. Michl, what happens if you save those images in PNG format?
You are right, the debugger shows for PDest RGBA [0,0,0,0]. Interesting, the result is a complete empty png, not just empty at the black areas.
[Edit]
PSrc1 and PSrc2 have values, but alpha is all the time 0.
If I load a bmp, alpha is all the time 255.
If I fill the alpha channel for the jpg, the example is running fine:
procedure TForm1.FormCreate(Sender: TObject);
begin
FBitmap := Nil;
Picture := TPicture.Create;
Picture.LoadFromFile(Application.Location + 'test.jpg');
WriteLn(Picture.Bitmap.PixelFormat); // write for jpg and bmp: pf24bit
Dummy := TBGRABitmap.Create;
Dummy.Assign(Picture.Bitmap);
Dummy.AlphaFillRect(0, 0, Dummy.Width, Dummy.Height, 255); // <- this line added