When using Kast, you need to have kasting permissions in a party in order to stream video & sound.
When you join a party and don't have access yet, the buttons will look like this:
As the tooltip suggests, a good way to start is to ask for streaming access in the party chat. The group owner and moderators have the power to give you streaming rights.
Send a polite note in chat, and tell them you have some awesome videos of dogs falling into swimming pools that you just have to show them. Like this:
Once the owner or moderator has given you access, the buttons will no longer be greyed out, and you will be able to share your screen and audio with everyone else. The buttons will look like this:
Now, just click the button on the far left side to share your screen, and click on the microphone icon to unmute yourself and broadcast your audio.