For Xbox there will be a 2.71gb update, when that’s done open Infinite, go to campaign and it can be downloaded from there.
Not sure about PC, maybe restart to see if update shows
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For me on Series X, I went to manage game in games and apps, clicked on the updates section and there was a 4gb update waiting. After I started that, the campaign add on appeared in the management section and I just added it to my download queue and it increases the 4gb update by 22gb. Didn’t need to launch the game to start it going 
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For me it was a 4GB update, but can confirm the rest. Series X
If it helps anyone I’m using the Xbox App on PC (Gamepass) and had to restart my PC for the app to offer an ‘update’. After that, plain sailing
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im at work, I did the 2.5gb update, but gotta open the game, 8 hours more to go home 
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STEAM USERS
Restart Steam completely!
If that does not work, open the DLC tab, uncheck the Campaign, retart again and you should see the full Campaign ready to download if you recheck that box!
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Thanks. Nice to have wasted 30 min trying to figure this out.
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great I´m doing that
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Best of luck! I should be playing within 30 minutes 
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Thank you for explaining how to download. 
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On Series S, it works! That was a big help. Thank you.
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