Thanks again to you all,

We have actually built the stream ourselves, helped with some tricks got from the internet, and it seems to work within our test environment. Here is the pseudo-code for memo:

Method OnRequest(request As %Library.Persistent, Output response As %Library.Persistent) As %Status
              set httpRequest = ##class(%Net.HttpRequest).%New()
              set httpRequest.Server = "(...)"
              set httpRequest.Port = (...)
              Set filename="(...)"
              Set file=##class(%File).%New(filename)
              Do file.Open("RU")

              Set sc=fileStream.CopyFrom(file)
              Do file.Close()

              do fileStream.Rewind()

              set myStream = ##class(%Stream.TmpCharacter).%New()           
              set startJsString = "{""document"":{""id"":""@GUID@"",""language"":""fr"",""patient_id"":""@NDOS@"",""doc_type"":""@DOCUMENTTYPE@"","    //...and so on
              set startJsStringData = $REPLACE(startJsString, "@GUID@",,     1, -1, 1)
              set startJsStringData = $REPLACE(startJsStringData, "@NDOS@", request.patNdos ,     1, -1, 1)
              //...and so on          

            do myStream.Write(startJsStringData)

            s startJsContentString = """sections"":[{""section_id"":""main"",""content"":"""
            s endJsString = """}]}}"

            do myStream.Write(startJsContentString)
            set sc = ..Base64Encode(fileStream, myStream,,1)
            do myStream.Write(endJsString)
            do myStream.Rewind()        

            set len = 32000
            While (len > -1) {
                set sRead = myStream.Read(.len)
                do httpRequest.EntityBody.Write(sRead)

            set sc=httpRequest.Post("/index/push", 0)


ClassMethod Base64Encode(tIn As %Stream.FileCharacter, tOut As %Stream.TmpCharacter, chunk As %Integer = 32000, Flags As %Integer = 1) As %Status
   set sc = $$$OK
   if $g(tIn)="" quit $$$ERROR(5001, "Input stream required")
   if '$IsObject(tIn) quit $$$ERROR(5001,"Input is not a stream object")
   if 'tIn.%IsA("%Stream.Object") quit $$$ERROR(5001,"Input object is not a stream")
   if 'tOut.%IsA("%Stream.Object") quit $$$ERROR(5001,"Output object is not a stream")
   set chunk=chunk-(chunk#3)
   do tIn.Rewind()
   While 'tIn.AtEnd {
    set sc= tOut.Write($SYSTEM.Encryption.Base64Encode(tIn.Read(chunk),Flags))
    if 'sc Quit
   Quit sc

Best regards