If you're just sending text lines, then it's not hard to accumulate the incoming characters into a buffer and then dole them out when you have a complete line, eg:
Dim TextBuffer As String
Sub AStream_NewData (Buffer() As Byte)
TextBuffer = TextBuffer & BytesToString(Buffer, 0, Buffer.Length, "UTF8")
Dim EOLChar As String = Char(13)
Do While True
Dim EOLCharAt As Int = TextBuffer.IndexOf(EOLChar)
If EOLCharAt = -1 Then
Exit
End If
Dim TextLine As String = TextBuffer.SubString2(0, EOLCharAt)
TextBuffer = TextBuffer.SubString(EOLCharAt + 1)
HandleTextLine(TextLine)
Loop
End Sub
or if you prefer clarity over efficiency, you could change this bit:
Do While TextBuffer.Contains(EOLChar)
Dim EOLCharAt As Int = TextBuffer.IndexOf(EOLChar)