The clock and watch screw article is really good but it is I feel aimed at clock people Like my self who make clocks. So I would like to fill in the little but important things that have been left out. Firstly clock and watch screws are made from high carbon steel like drill rod, this of course takes to heat bluing perfectly. Now a top class maker polishes the screws then coats the screws with a mix of water and Fullers earth before heating to cherry red and quenching, this clay stops the steel surface from oxidising and loosing its fine polish. Then the screws are re polished then heated again to obtain that clockmakers blue. But the article did not say that the blue colour is a type of oxide and the slower you bring the steel up to the blue colour the thicker this layer becomes and the finer the blue colour is.
If you are using basic steel screws and want that clock blue colour the standard method is to case harden the screws first by using a product like Kasenit then polish then flame blue.
Hope this is of further help.