Short film ideas are very specific because the course of the story has to begin and end in a very brief period of time. Thinking of an longer film idea is often much easier because it can remain vague. Getting ideas for a short film is a much more difficult process since the idea itself will often be the entire screenplay. Here is a look at getting ideas for a short film and how you might develop your own short film ideas.
Getting ideas for a short film are often secondary to creating characters in detail. These characters will often drive a short film, even more so than with feature films because you can center the entire film around them and their changes. A short film idea can then emerge from just trying to create a fully realized character with a complete backstory and personality. Try constructing a character biography for them listing all of their physical attributes, their political and religious beliefs, their family situation, their goals, their biases. Anything else that'd create a full human being. You'll likely be able to complete your short film idea right from what you've put on the page.
Most narrative films start with the presentation of a problem and then allow the rest of the film to complete that problem, allowing the characters to grow along the way in a way that transcends the original problem. This is the same in a short film, though oftentimes the problem is either much more specific or much more simplified. A great way to develop short film ideas is to try to think of different problems that are both very singular and correlated to themes you'd like to explore.
Short films are often not restricted to the same forms that feature film are because they lack a conventional commercial infrastructure around it and because the short length allows you to try things that may not work for an hour and a half or more. This allows you to express experimental ideas that are based around creating visuals, including performance art. Essentially creating films that are different than anything that's come before. If you're looking for short film ideas like these then you may have an easier time than with narrative films because you can just think about themes that are important and try to correlate different items that don't have to be structured together by story or characters. You also don't have to decide exactly what your short film idea is until you're in post-production.
Short Documentary Film
If you're thinking about doing a short documentary film you're again going to have to consider simplifying the topics as much as possible. For your short documentary film you may want to think about either profiling an individual you find interesting or an even, that way you've a very identifiable topic that you can expand on in the short form. Since documentary film tends to take a lot of waiting and you may not want to have to deal with this during the production of your short documentary film then you should choose topics that aren't going to require any difficult contacts or waiting.