Without knowing the actual optical quality of your particular 55-250mm lens, I'll just stick to commenting on the focal length - in general, yes - you can pretty well fill the frame with the castle from the train station if using a 250mm lens on a cropped DSLR body (like a 'Rebel'). In fact, you'll probably only need about 120-130mm of focal range.
And yes, that focal length should be fine for Kilimanjaro as well - sometimes, you'll have animals too close, and won't even be able to get them in the frame - most will be fine, and those that are more distant should be just about right with the 250mm lens. Most of my Kilimanjaro shots are taken with 18-250mm lenses, and most shots seem to be between 130mm and 210mm. As Kenny mentioned, the blur has more to do with keeping your shutter speeds high enough to compensate for the animals moving and for your safari truck bumping around - even stabilization isn't always a cure for the truck's movement, and doesn't help at all with moving animals!
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To avoid blur, mostly try to keep your shutter speeds to 1/500 or higher, and you should be fine. Use stabilization if you have it, as it can help with some of the minor hand-shake and movement on the truck, but mostly keep the shutter speeds up.