Generate and Download document from external system in single click in Appian

There is no solution I would want to recommend to make this work.

Agreed with Stefan - this sort of thing really requires a 2-click approach to maintain code cleanliness, maintainability, flexibility, etc.

You cannot do it in single click but you can have 2 links

1. Fetch Document - Link to call the integration and bring the documents inside appian using dynamic link

2. Click to Download - Link to download the document using document download link

Step1 : Create a process model to download and store the document in a folder. 

Step 2 Create a Post webApi to trigger this process model and this webApi should return the documentId of the downloaded document

Step 3 Create a integration object to trigger this webApi and this should be just returning the documentId again

Step 4 Create a get webApi. In this webApi call the integration object and in response use 

a!httpResponse(
statusCode: 307,
headers: {
a!httpHeader(name: "Location", value: local!redirect)
}
)

where local!redirect : document(documentID,"url").

Step 5 : Call this webApi as a link in your interface.