saving project on flash memory

It's possible. However, the maximum sustainable write speed of most USB flash drives is a huge issue: Most cheaper USB 3.2 Gen 1x1 flash drives write at slower than 50 MB/s - a huge issue for direct exports in Premiere Pro. That's much slower than even an external mechanical spinning hard drive!

Worse, you may have a USB 2.0 flash drive that writes at only 4 MB/s!

And out of all of the flash drives on the market to date, one of the very few flash drives that is appreciably faster than a HDD, and thus fast enough for some types of exports, is the newer versions of the SanDisk Extreme Pro USB 3.1 drive (the ones made after Western Digital bought the company). Unfortunately, that drive uses a USB-A connector, which requires a USB-A to USB-C dongle from Apple to even work at all on your MacBook - and even that flash drive has slightly slower write speeds than a typical SATA-based internal SSD.

And the 2020 MacBook Air came in two versions: Early 2020 (which still used Intel processors, but were updated to the 10th-Gen Ice Lake architecture) and late 2020 (the first Apple Silicon M1 model). The two USB-C ports on those models also supported Thunderbolt 3; however, in USB mode were limited to USB 3.2 Gen 2x1 (10 Gbps, or about 1.23 GB/s).

Under the circumstances, I would recommend one of the external USB 3.2 Gen 2x1 external SSDs which have rated speeds up to 1050 MB/s instead of a molasses-slow USB pen drive (most of which are even smaller in capacity than the available internal space on your MacBook Air's internal SSD) for that MacBook Air. 

Performance will not be very good. Even with just the one 256GB drive, will not be that great. It may work, but not well, especially if it's a 'big' project.

yes, you can save production files from any app on an external drive.

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