The phrase "burnt with" is correct and usable in written English.
It is often used to describe someone who is experiencing a strong emotion such as anger, sorrow, or excitement. For example, "She was burnt with jealousy as she watched her ex-boyfriend with his new lover."
For boys, two had burns from contact with a silencer (muffler) on a four wheeled motor bike, two were burnt from a hot water bag bursting, one was burnt while playing with petrol and fire, and the remaining boy was burnt with hot oil from a BBQ.
Myself age eight, whole head burnt with embarrassment at having lost a library book.
Another plane in Pennsylvania Crashed in an empty field Everyone was burnt With courage they resisted.
I even choked down the donkey -- thick and burnt with a very gamy aftertaste.
In custody they also discovered his body was covered with scarring "consistent with having been burnt with boiling liquid".
Poetry: "Myself age eight, whole head burnt with embarrassment / at having lost a library book". is my heart.
When the police finally recovered the boys they were malnourished, and had been whipped and burnt with cigarettes.
Yet Hussain was arrested, burnt with cigarettes and had three fingernails extracted to force him to confess to killing a child, his lawyers say.
Ore containing minerals is burnt with acid to free up the copper but the heavily polluted waste has been pumped straight into the Luilu river.
Plenty were burnt with too much unsold stock from "over-merchandised" movies such as "Godzilla" and the more recent "Star Wars" episodes.
In other places the dried reed beds caught fire and burnt with such heat that the ground has been baked into a hard ceramic crust.
