I too am very interested in how Discourse chat will relate to Discord as many, many communities seem to have both (including several that I admin or interact with regularly). As a person who really had to get used to Discord and make peace with the fast flow of info, as well as the semi-loss of interesting discussion that often results (not because it’s truly erased, it’s just very difficult to find and “surface” in Discord after a while), I have an initial strong impulse to try to move everything away from Discord and a hope that Discourse chat reaches reasonable feature parity with it to make that possible. 
However I recognize other people have different preferences and biases than I do, and in any case any forced approach to making such a migration happen would likely not be well received and could easily be damaging to the existing community.
I’ve discussed previously a wish for better integration between Discord and Discourse for these reasons:
And in general I am very interested in the interface between sync (chat) and async (forum, etc.) discussion. I think Discourse has the best opportunity to blend that here, so the integrated chat feature is super exciting.
Perhaps the best chance of making a more natural progression from Discord to Discourse chat is simply to make Discourse chat really frickin’ good. So far I’m impressed with the early progress, but I know there is a lot to chat functionality, and it will likely never be a major priority for the team (maybe I’m wrong about that). I do think that perhaps Discourse chat might be more natural and easy to migrate to in communities where there is an active Discourse forum, and Discord was not the original platform, and/or was chosen at some point as the real-time option simply because it was free/easy to setup.
To get a bit more specific, this is my current thinking for how to handle things in two of the communities I admin:
Productivity Community
- Started on Discord
- Forum setup by myself and another admin to capture larger insights from Discord
- From the beginning the forum has had comparatively low activity vs Discord
This is an interesting one because, as noted, it began on Discord. So there is definitely a lot of “gravity” to that space for many community members. However activity has been low the last several months on both Discord and Discourse. We also have had notable issues where incredibly good discussion happens in Discord chat, and is very hard to move over to Discourse discussion (where it arguably belongs due to how in-depth it is, and how useful it might be to preserve for later reference, engagement over time, etc.). The already quite good Discourse chat function to move a set of messages to a new or existing topic is like a dream come true.
So although it’s not exclusively my decision to make, due to the low activity in both areas I am tempted to try to move primary engagement over to the Discourse forum, making heavy use of chat, with the forum topics reserved for more long-form stuff, and the fluid interface between the two making it all work more comfortably. But that’s certainly easier said than done. The Discord login integration in Discourse may help though…
Software Product Support and Testing Community
- Started on Telegram
- Discourse (originally Flarum) was added early
- Discord added much later, still modest levels of activity, in bursts, and shared with Telegram
This community is connected to a security/privacy-oriented productivity app, and already many of the users have been complaining about the use of Discord. Telegram was originally used in part due to privacy concerns. However Telegram’s capabilities for managing groups, roles, etc. is frankly terrible. That was part of why a move to Discord was started. Now that chat will be available in Discourse itself I am hopeful that the primary, official chat channels can all be moved internal to the forum instance. That would be a big win, I think, because it would simultaneously address both the privacy issues of Discord, and the management issues of Telegram, while also further centralizing communications into a more unified and powerful system. That should save the team a good amount of time. Likely both the Discord and Telegram channels will continue to exist, and the team may need to find ways to smoothly hand-off their management to trusted community members, while making clear that they are no longer official channels… This is just my personal hope and vision, it’s not solely my decision to make, but this is the approach I’ll be advocating for. 
So to my mind there are advantages for both admins and users, but the primary advantages currently are for admins who want to centralize. In order to drive adoption by users I think the chat feature will need to be as robust and easy to use as possible. I do anticipate a bit of an uphill climb convincing users in at least one of these communities to move over.
So, I don’t have any particularly insightful answers. Just musing about it all. But I wanted to contribute to and encourage this discussion as I am also keenly interested in how people will handle this, and what resources, features, etc. they feel will best enable them to do so effectively.