Currently, Discord is only available for voice chats on Xbox and screen sharing is not possible. However, in a blog post it published, Discord announced that they have started rolling out game streaming on Xbox for Xbox Insiders. The feature will be rolling out to all Xbox users soon. The exact date is not yet known.
How to stream games on Discord from Xbox?
To connect to Discord from Xbox, you must first connect your Xbox and Discord accounts. To perform this operation, you must access your Discord account from mobile or desktop and go to User Settings > Connections. You will see the option to link Xbox and Discord accounts from the Connections menu. From here you can link your Xbox account to Discord. Once the process is complete, the user needs to be signed into the same Discord account on their Xbox as well. Discord will then show the Publish your Game to a Discord Server or DM option.