The flag looks like an image format, if so, Photoshop would be the better choice, make a path of the star area, make a selection, using the path, adjust the selection (Image> Adjust> channel mixer> black channel into cyan & Magenta).
Are you sure it's a vector file?
Perhaps those are separate paths, you can check out the layers panel for that.
It might be grouped.
It might be a compound path.
I would separate it. Although it would be possible with a vector file. You could just use the erase. But you would get a somewhat straight line, which would look kind of strange.
I would use the brush tool and take a brush from the "Artistic" section of the brushes libraries.
Draw some lines so you get a somewhat organic look. Move all of those lines below the flag shape and then make a clipping mask.
How to analyze your clip art:
I agree with Luke that it looks like a raster image, and that it would be natural to use PS.
You could also make sure, including whether it is possible to choose a vector version if both are available.
The following is based on a raster image dealt with in AI.
Owing to the thick red lines, it is hard to guess the exact appearance of the desired border between black and blue, and whether there is an easy border with black meeting white. Apart from that, there are some grey smudges in the star part.
If you are able to draw a closed path that includes the black parts to become blue (it can be drawn freely in the white space at the top and left, maybe also at the bottom of the star part, so the crucial parts may be where the stripes meet the star part from the right), then you can (also) try to:
1) Draw that path on top of the image and give it the desired blue colour as fill;
2) Copy the blue path behind itself (Ctrl/Cmd+C+B);
3) Copy the original image on top of the path from 1), you can select it and use Ctrl/Cmd+C+F;
4) Select both the image from 1) and the blue path from 2), then in the Transparency panel (flyout) click Make (Opacity) Mask with both Clip and Invert Mask ticked.
Edited: The addition of 3) ought to unsmudge the smudges (prevent them from remaining smudgy/greyish).