Kast provides a party link sharing to invite friends into parties. You can find the invite button in the top right corner when you hover over a video in the party view (see images below). You can also find the invite link by clicking on the party name to access the party information dialog.
Invite button, top right.
To invite friends into the party use the "Invite Friends" button at the top right to open the invite modal (see picture below).
After selection you have two options to invite your friend.
1. Use the search bar to find any Kast user and select "Invite"
2. Copy the share link at the bottom and paste the link to the direct messaging or social media service of your choice.
Currently you can only share invite links from the desktop app, not the mobile versions of Kast (but it's coming soon!). Right now on iOS or Android, you can discover public parties, accept friend invites and get together privately by following a direct share link from a friend.