You might wish to take a look at my list for Filetransfer between two Android devices – I'm sure you'll find your candidate there. And I'm pretty sure it will be something like...
SuperBeam, which makes use of NFC (if available) or QR-Codes (otherwise) to connect two devices, and then uses WiFi-Direct for the transfer itself. So it's easy to connect – and much faster than Bluetooth:
SuperBeam (click images for larger variants)
As the screenshots show, it's pretty easy to deal with: On the sending side, you select what to send and how to initiate the transfer – and on the target device (which also must have the app installed), you select the same connection method: either scanning a QR code, or hold the devices close to each other and use NFC.
It's possible to use SuperBeam on the sending side even if the target does not have the app installed – but that would involve a web service, and thus contradict your requirements. Speaking of which:
- No network: Taken literally, I had to recommend an SDCard ;) But: No internet connection required, it uses WiFi-Direct.
- Reliable, using checksums where needed: I don't know about the "internal handling", but all I've heard was positive feedback. So it should be reliable – however it does its job.
- Runs on Android: Yupp, it's an Android app.
- Open Source: Afraid that's the only part the app does not match. Moreover, I'm afraid that's the part hard to match: Though my above mentioned list covers 13 candidates currently, none of them seems to be Open Source – and I've not heard of such. Though I must admit the fact simply slipped by when I investigated on that topic.