Nexus 7 (2013) OTG cable with flash drive doesn't work

I just bought a Nexus 7 (2013) and an OTG cable. I wanted to connect a flash drive to it. When I connected it, nothing happened. I tried to find the folder with my flash drive contents in /etc - there was nothing about my flash drive. I searched in /storage/emulated/0 - there were contents of my internal SD card. I downloaded some applications from Google Play (e.g. Nexus Media Importer, OTG disc manager). It worked, but only for reading. Is there a way to write to my flash drive? Please notice that I DON'T want to ROOT.