Can I use the word "Kerfuffle"in formal writing?

Solution 1:

Can You use the word “kerfuffle”in formal writing? YES. Vocabulary.com

A kerfuffle is some kind of commotion, controversy, or fuss.

As in:

You tell your little girl everything will be okay, or you tell your tween how to handle a friend kerfuffle, or you commiserate with your teen who’s complaining that his teacher hates him. Washington Post Aug 21, 2019

And from WorldWideWords:

Though the White House spokesman Ari Fleischer used it in January 2002, it hasn’t been especially well-known there and a later presidential usage caused something of a kerfuffle:

President Bush used “kerfuffle” Monday during an appearance in Ohio, and in so doing, he created a minor one himself. Some of the president-watchers on duty in the press gallery had to stop in mid-story and explain to America this novel new word from the man who gave us “misunderestimated.” The Lima News (Ohio), 22 Mar. 2006.

Listed as informal in BrE, In AmE it is not always so designated. AmE is also 'looser' than proper BrE, for better or worse. My sense is it can be used formally or informally, at least in AmE. Now 'bloody hell' ... that's another kerfuffle, and it not over the use of hell.

Solution 2:

The term is certainly informal.

Kerfuffle:

You will most commonly come across this wonderfully expressive word for a commotion or fuss in Britain and the British Commonwealth countries. It is rather informal, though it often appears in newspapers.

(worldwidewords.org)