It really isn't hot oil bluing... hot oil does not impart blue to steel.
Flame bluing is as described above in post 3.
Polish the metal very smooth and bright... heat slowly and carefully with a flame... the first colour to appear will be a light straw... now be careful as too much heat will run through the colours too fast to retain what you may want... light straw will go to a darker brown and then light blue/purples will appear... I like to stop at a nice blue by removing the heat source, but if you have had a bit too much heat there the colours will continue to change... so you could dip in in oil to lower the temperature and stop the colour change. Perhaps this is how you refer to it as hot oil bluing?
The best way to try this is with a steel screw head... prepare it and then heat it and see how the colours change... re polish and do it a few times...
"blue" done this way is not very durable. It looks good on screw heads though.
I have a chart I copied from old gunsmith book - they used to use the colours as a temperature guide - so brown means 500 F, purple colour means surface about 540 F. Next comes Dark Blue at about 590 F, then Light Blue about 640 F, then Grey-Blue about 700 F. As mentioned - the piece will have heat inside - the colours are about what temperature the surface is at - quit with the heat source, can still get hotter because of residual heat inside - torch flame is much, much hotter than the colour that you are trying to produce. So, needs some experimenting - some practicing - with large or hollow pieces - and then the product is still kind of second or third rate for the use...