Hi!
Many things can burn fiercely, but the phrase is typically reserved for passionate emotions such as hatred or love, though it can also be used to describe actual fire.
Examples:
"Their love for each other burned fiercely."
"The hatred in his eyes burned fiercely as he looked at his enemies."
"The wildfire is burning fiercely."
As a combined phrase, it is usually used only in literature, but it can be used in spoken English in certain contexts.
Hope this helped!
Ide