Following are the instructions according to esri's Use offline basemaps help topic, augmented by additional screenshots. This assumes that offline basemaps have already been created, according to this solution.
Download a linked map package in the Survey123 field app
To download a shared map package, complete the following steps:
Start the Survey123 field app and sign in with your ArcGIS organization account.
Select the survey to which you associated a map package.
Choose the menu and choose Offline Maps.
Choose the map package from the list to download.
Once it's successfully downloaded, you'll see the map package in the list of basemaps on the location page of your survey.
Use a map package in the Survey123 field app
You can use either manually copied map packages or downloaded, shared map packages in your survey.
To use a map package, complete the following steps:
Start the Survey123 field app and sign in with your ArcGIS organization account.
Select the survey to which you associated a map package.
Choose Collect.
Choose the map question and display the full-screen map.
Select the Basemap button and select your map package.
