can i back up my phone on a flash drive?

No. You can make a backup on your MAC/PC disc, then you can copy that backup to a flash drive.

See also this guide:

Locate backups of your iPhone, iPad, and iPod touch - Apple Podpora

In 1st section, read very carefully the 2 points.

Regards

Giulio

Not directly.

You can backup the iPhone to iTunes on a computer and then copy the backup out onto a flash drive. but there's no way to backup directly to a flash drive.