The demon slayer boots are a pair of boots specially tuned for fighting demons. It is dropped by Kal'gerion demons or a demon boss as part of a Demon Flash Mob, which will show up at a number of places every full hour. There will be a message in your chatbox describing the location of the Demon Flash Mob when you are level 120 combat or higher. It requires level 60 Ranged to wear.
Wearing the demon slayer boots while killing demons on a Slayer assignment will give a 1% increase to Slayerexperience gained during the task. Equipping a full set of demon slayer equipment will give an 8% total increase to Slayer experience gained while on the task. Wearing the boots also grants a 2% experience boost in the chosen combat style, as well as 4% damage boost against demons.