Samourai Wallet has built-in signature generation to prove control of a bitcoin address private key without revealing the private key to anyone. The list of current unspent outputs contains a list of addresses that can sign messages in your wallet. Currently you can only sign messages with addresses that contain an unspent balance of bitcoin.
Step 1 - Show unspent outputs
Tap the three vertical dots on the top right of the toolbar and then tap Show unspent outputs. This will launch a list of current unspent outputs in your wallet.
Step 2 - Select the address to sign from
Tap the unspent output that corresponds with the bitcoin address that you want to sign the message from. This will bring up a screen with details about your UTXO.
From this screen, tap the options icon on the top-right of the screen to bring up the Advanced options for that UTXO. From there, tap "Sign Message" to sign a message of your choosing.
Step 3 - Enter your message
Enter the message you want to sign in the textbox, and press YES when finished.
Step 4 - Copy and share
Copy the signature and share it as needed.