Copying on paper is highly discouraged. For example, if it comes into contact with water, it will fade, and it could even be eaten by mice or termites. I keep the key on a flashdrive.
Archival grade acid-free paper is a thing. Archival grade ink, ballpoints or even good pencils are a thing, too. If someone uses crappy paper and ink that fades, it's their fault.
Your local environment, especially humidity, plays a big role for longevity of your analog paper backup. If your local conditions are not suitable, then use something that doesn't degrade in humid environments. Some suitable steel aljoys and Titanium don't degrade under humid conditions.
You keep your key(s) on a flashdrive, until the flashdrive fails which is not something unheard of. In my humble opinion, you're playing with fire.
And there could be more issues with your process. First, your key has to touch a device to copy it on the flashdrive. Was that device a "cold" one ("cold" means, it was never online, never touched the internet, never will touch the internet after seeing your key)? If the device was online or will become online again, you can't be sure your key remains safe.
Second, flash media stores data by trapping charges. Those charges can dissipate over time out of flash cells. The retention time depends heavily on the quality of the flash chips, storage conditions and type of flash cells (SLC has usually better retention than MLC or worse QLC cells). You can't reliably store data on flash media over many years without ever refreshing the flash storage. Refreshing the flash storage exposes your key again to a device that is hopefully clean and "cold", but also is an opportunity for the flash device to fail because most electronics are not built for eternity.
Cheap flash drives commonly use B- or C-grade flash chips, or worse. Don't expect archival retention time from this stuff.
I've no empirical data. I lost very few flash drives somewhat like out of the blue. Can't really remember what it could be. I'm maybe biased but it could be that it were flash drives that have been laying around for really long time, some maybe a few years. Can't tell for sure, though.