They shouldn't store the images on the phone. You should be only able to view the image immediately after downloading it. After 10 seconds of viewing the image, everything gets deleted from ram.
Snapchat was designed for ephemeral communication, not secure "send-and-destroy" messages. It would be very foolish of them to market it as something it cannot possibly be.
This is an okay compromise tbh.
(They could offer a super secure option or whatever, I guess)
(I like security.)
But it doesn't work, since you need some way to generate new API keys for your second device... which could be a Bad App.
If you 1) enforce one key at at time (so one "device" at a time), 2) rate-limit key changes (if you switch to a new device, or Bad App, you can't switch back within a day or two) and 3) eliminate Bad Apps in the app stores- you effectively limit Bad Apps to being entirely web-based, and hopefully the restrictions on webapps will make the Bad App sufficiently a pain in the ass to use that people won't want to switch to it, even though it lets them save photos, since it locks them out of the real app.