The Victorians had special machines to floss their corsets in factories, but these days we have to floss our corsets by hand and a variety of materials can be used. I love flossing corsets, I find it extremely relaxing and it makes the resulting corset feel really special. My favourite is self coloured flossing where the flossing thread is the same colour as the corset - this is quite a modern iteration of corset flossing which gives a really elegant and understated finish.
I have found that John James Embroidery needles are best for flossing because they are uber sharp, smooth and sturdy. You may need some bees wax or dressmakers wax to strengthen your embroidery floss. Draw the thread through your beeswax, then iron the thread so that the beeswax (or paraffin for vegans), sinks into the fibres. This isn't always necessary, it depends how fine your thread is. A multi-ply buttonhole type thread wont need this treatment.
As for what thread to use for corset flossing - there are lots of options. Button hole twist thread or "top stitch" thread (the same thing) is the most easily available and comes in a huge array of lovely colours. It is very strong and durable, easy to use and doesn't cost the earth. The other good type of thread to use is perle cotton which comes in various thicknesses, or pure silk thread, preferably multi-stranded - this is harder to come by and can be pricey - you do get a beautiful lustre with it though. You can use regular embroidery thread but in my opinion, it really isn't strong enough for corset flossing. Linen thread is an 'authentic' thread to use for older styles and also comes in a variety of colours. Linen thread often needs conditioning with beeswax thread conditioner.
A measuring tool is handy for ensuring that your flossing designs are regular - both in the same place on the corset, and the same size over the corset. Watch the video for a cunning trick to make a failsafe template without the use of a ruler or other external marking tools.