Crop the flag in a bitmap editor (GIMP, Paint.NET, Photoshop, etc...) to its exact rectangular size. Then you haven't any background to remove. Every pixel belongs to the flag. Trace without removing the background.
Of course it can happen that your flag is a photo which is taken when the flag is waving and it cannot be cropped. In that case a little more is needed. Import the image and do not scale it smaller. You need the original size. Scale it after the process is done and you have a vector image.
At first make a spare copy to the artboard. Trace (see NOTE1) the imported image in colors without the background. Shift the tracing result (with holes) aside and colorize the imported PNG to black (Filters > Color > Colorize):
Select the blackened image, goto Edit > Make bitmap copy, delete the original blackened version. Now you have a real black bitmap, not the original bitmap with SVG function.
Trace in BW the black bitmap, remove the background from it, too.
Change the fill color of the black shape to white. Arrange it behind the flag with holes. It should fit within 1 pixel.
Ungroup the colored version. Group it with the white shape. The result:
NOTE1: If your image isn't pixel perfect 3 colors, but anti-aliased or a photo, you may need more colors than 3, I needed 4. There was 1 px wide light blue shape in the tracing result. I removed it with no harm.