I've tried the package in the elementary repos, and right now I have 20.04.2 installed from the flatpak. Both crash very easily, and the elementary package barely ran at all.
Currently on the flatpak, I am able to import clips and place them in the timeline. Effects, titles, and transitions work, though timeline playback is slower than I'd like. However, as the title says, it immediately closes the program the instant I click the save button.

I'm trying to switch from Final Cut Pro to free myself from having to use a 10 year old MacBook for all of my editing. I have also tried Shotcut, which crashes as soon as i try to open the import dialog. Whether that indicates some sort of system-wide problem, I don't know. Feel free to look at my my settings about page and let me know if you would like more information. Any help is greatly appreciated.

Please try with the current Kdenlive AppImage version 20.04.1b to see if there are any packaging issues https://files.kde.org/kdenlive/release/

If the problem/issue doesn't occur when using the AppImage, then it's your configuration or packaging.