The following worked for me (tested on react native 0.38 and 0.40):
npm install -g ios-deploy
# Run on a connected device, e.g. Max's iPhone:
react-native run-ios --device "Max's iPhone"
If you try to run run-ios, you will see that the script recommends to do npm install -g ios-deploy when it reach install step after building.
While the documentation on the various commands that react-native offers is a little sketchy, it is worth going to react-native/local-cli. There, you can see all the commands available and the code that they run – you can thus work out what switches are available for undocumented commands.