those kindle fire have other browser then silk browser? if the answer is yes. then probably majority of people are using Chrome even on Kindle Fire, in this case i wouldn't worry about it.
However if is must be done, then try exporting your game/app/website with a fullscreen mode Outer Scale. that way your game will fill the container its in. ! Important notice, the objects inside ur website at that point will be a bit larger and their position will be looking like is not where it should be thats because you have to adjust them based on the new fullscreen mode, or create a div that fits the entire website but restricts the construct app to sit at a surtain screen ratio.