Short answer: no (not yet).
UE does not have such a shortcut key for search results in the output window. For navigation you can only use the 3 methods described in the last paragraph of the help about the output window.
You can define a hot key to switch focus between output window and active edit window in the key mapping configuration dialog - command FocusToOutputWindow
And Finn Ellebaek Nielsen has written a tool which can help you - see Find in Files -- Increase Edit Window Functionality
Since UE v15.00 there is Ctrl+Shift+Up to go within the document window to previous line according to previous line in output window and Ctrl+Shift+Down to go to next line in file according to next line in output window.
The keys can be configured at Advanced - Configuration - Key Mapping
by assigning something different to the commands OutPreviousMessage