Ensure the clipboard contents are stored properly on GTK

GTK needs to be told the data on the clipboard can be stored
before the store is attempted.

Also, document that the clipboard behavior on GTK is very
dependent on the configuration of the user's machine.

Closes #10515

src/gtk/clipbrd.cpp

@@ -306,6 +306,8 @@ selection_handler( GtkWidget *WXUNUSED(widget),
     if ( !size )
         return;
 
+    wxLogTrace(TRACE_CLIPBOARD, "Valid clipboard data found");
+
     wxCharBuffer buf(size - 1); // it adds 1 internally (for NUL)
 
     // text data must be returned in UTF8 if format is wxDF_UNICODETEXT
@@ -595,8 +597,19 @@ void wxClipboard::Clear()
 
 bool wxClipboard::Flush()
 {
-    gtk_clipboard_store( gtk_clipboard_get( GTKGetClipboardAtom() ) );
-    return true;
+    // Only store the non-primary clipboard when flushing. The primary clipboard is a scratch-space
+    // formed using the currently selected text.
+    if ( !m_usePrimary )
+    {
+        GtkClipboard* clipboard = gtk_clipboard_get(GDK_SELECTION_CLIPBOARD);
+
+        gtk_clipboard_set_can_store(clipboard, NULL, 0);
+        gtk_clipboard_store(clipboard);
+
+        return true;
+    }
+
+    return false;
 }
 
 bool wxClipboard::Open()