Well I will stick to what I actually know about it.
Satan's flame is basically a medium to extend you range during tai battle with the help of fire and not to mention because of fire it get's a greater damage dealing capacity too, The user of satan's flame can basically engulf his entire body in flame and use it as defense mechanism when is close combat battle or fighting a wind user and at the same time we can use that flame to deal damage, We can also concentrate are fire in specific area and thus make it more condensed and deal a large damage to the opponent and causing third degree burns to him.
How I would like to use it
Well I would also like to use it as speed enhancer in battle, I am talking about Tsuna's fighting style here we can basically shoots condensed flame from our hand or legs and use to either fly or makes us travel small distances like 3-5 meter in a mere second and thus in a close combat battle it becomes even more handy, We can even pass chakra in our leg's and shoot out continuous flame to fly in air all in all satan's flame is quite handy.