Earlier quoted context omitted.
I think they can run from cartridges, so if you have one loaded with homebrew games, they should work. Most Atari 2600 games had no copy protection.
Flashcarts don't work unless you devote the entire flash to a single ROM (some of them can do this). This is because the console snarfs the entire contents of the ROM into RAM first, rather than mapping the ROM directly into the CPU's memory space like the original consoles did. So the bank-switching tricks that flashcarts use to provide multiple ROM options on original hardware don't work on these. This is also why…
The console itself should never know the cart is not a simple ROM with some bank-switching logic. Since Flash (or an SD card) isn't ROM, the ROM image will always be loaded into the cartridge RAM by the microcontroller software. There were many different strategies back then, so the ROM would need to have a file attached telling the on-cartridge microcontroller how bank switching worked on that title.
All you'd need is some UI to make it easier to switch between titles.