How can I put my iPhone in discoverable mode?

How can I put my iPhone in discoverable mode?

You can't

Find an app.

It's already discoverable, whenever Bluetooth is on. That's how iPhones can find each other for AirDrop.

"Discoverable mode" is mode closely associated with the need to pair a new Bluetooth device (unless you are looking to do something else). To get into this mode you simply go to settings-->Bluetooth. As long as the iPhone is unlocked with this screen open the iPhone is discovable to new Bluetooth devices.

Once bluetooth is on, it is in that mode.