Can you use a usb flash drive as a memory drive with a picaxe microcontoller?

I want to know if you can store code and scripts on a flash drive and have the flash drive connected to a microcontroller and have the microcontroller load the code.

No, a PICAXE can't work as a USB master without extra hardware and software support - look at Maxim's USB host chip, the MAX3421 for example.