I couldn't see the attached example but a little image-Googling made me guess it's the 2013 Denver County Fair poster. If it is, that effect can be done in Inkscape. Here's one way to do it:
Make 2 different gradient filled "rays" per sunburst. The angle of the pennant shapes depends on how many rays of each you want in a sunburst (9 degrees in this case, with 20 of each kind of ray per sunburst).
First, move a pennant's center of rotation to its tip twice until the rotate and skew controls appear, move the cross rotation point that also appears to the pointy tip [snap to cusp nodes to make this easier]).
- Use the transform tool (Shift+Ctrl+M) for duplicating and rotating the cloned pennants to make a sunburst. Group the rays once a sunburst is complete. You need a yellow and a red sunburst
- Clip the sunburst by placing your desired shape (rectangle in this case) on top of the sunburst, right clicking on them, and selecting "Set clip".
The yellow sunburst clip group below is more fancy. It has a white background shape on the bottom to prevent the red sunburst from showing through and muddying the colors), a dark green "mountain" shape above it, and the yellow sunburst (made slightly transparent) on top -- all grouped together before clipping with the "inner frame" rectangle.
You can also tweak the gradient of the original rays to have effects like this: