This is traditionally the worst UX problem with Signal / Session / Matrix etc. Manually handing keys back and forth is a disaster. Compare that to something like Telegram or WhatsApp where you can just log on and everything is there.
You can read more about Swarm here: https://jami.net/synchronizing-conversation-history-with-swa...
To add a new device, from account settings select 'Link another device'. This will create an encrypted archive of your account details and temporarily (for 10 minutes) put it on the OpenDHT network, and give you a PIN which you would use on your new device to have Jami retrieve and import your account. You could also do this manually and without going through OpenDHT, by having Jami create a local backup of your account on your current device, and then transfer the backup archive onto your new device yourself, and import it into Jami. After adding the new device, your Swarm conversations and their histories will begin synchronizing shortly.
They're doing cool enough stuff that it seems like they could attract real attention eventually though.