I just create a web app buid map and feature layer I want to add separately from another server.
You can add content to a AGOL map via the rest endpoint from your ArcGIS Server. Use Add > Layer from Web, copy and paste the URL and away you go.
You could opt for Portal for ArcGIS, which is an in-house cloud. All the shared data would be stored in your organization's storage/premises.
About Web AppBuilder for ArcGIS—Portal for ArcGIS (10.5) | ArcGIS Enterprise
You could just use an "empty" web map as the starting point for your web app, then use the Add Data widget to add your web services.
Hope this helps,
If you are using the web AppBuilder developer edition, check out LocalLayerWidget Version 2.5 and AccessifizrWidget Layer - 09/28/2017
this and other widgets and related blogs can be found Web AppBuilder Developer Edition - Resource List (updated 5/13/2018)
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