>> Note that you are trusting this app with your private key.

On Android, the Kryptonite code uses the AndroidKeyStore to store the private key, which means that the app does not have access to it. At a minimum (on old devices), AndroidKeyStore keeps the private key material in a separate process, so it never exists in the app's process space. On newer devices (launched with M or later), the private key material is kept in the Trusted Execution Environment, so nothing in Android user or even kernel space has access to it.

EDIT: Actually, there's one small flaw in the Kryptonite code that may make the private key accessible to a sophisticated attacker who compromises the app. The key allows signing without using a hash function. Signing a sequence of carefully-chosen plaintexts can reveal the private key. I filed an issue and sent a pull request.