When writing an outline for an informative speech topic that involves stages or a process such as "how to fix a flat tire,"is there any other organization pattern to use besides chronological? It just seems to me that topical, cause/effect, spatial, or others just won't fit the topic.

That is a good question. On first glance, it would appear you're right. Since most processes are chronological, a chronological order would be the most common organizational structure.
It is not the only organizational structure possible, though. One of the easiest alternative structures to apply, and one that can make a stage or process speech more interesting, is a narrative. You can tell a story that illustrates the stages or processes by vividly recounting actual stories of people going through those stages. Rather than just explaining the steps to become a doctor, you'd tell stories about medical school and residency.
A cause-and-effect structure could also apply. If you used this structure, you'd give the causes for following a specific process, and the effects of doing so (and, if you have time, the effects of not doing so). This can be useful for processes with a number of options, like how to plant a garden.
A spatial structure is useful if the process has spatial implications or details. You can see this clearly in discussions of how to organize your life. You have to organize different spaces (such as your car, bedside, and wallet), and these different spaces might require different processes.