Should three-fifty be hyphenated?

In US English and British English, "three fifty" would not indicate the number 350 without significant context contributing to that interpretation. It would indicate the number 3.50, typically in terms of money ($3.50 or £3.50). And in these contexts, it would not be hyphenated.

Both the example given in the question and the examples of money are themselves not formal language, though, and would therefore not necessarily follow traditional rules of grammar. Language is a flexible device, and for writers of novels, short stories, and novellas, poetic license often trumps grammatical correctness. The foremost question to an editor's mind should be one of whether the meaning of the writing is clear and whether the style fits the presentation holistically.

To be grammatical, one should say "three hundred fifty." Further, to express £3.50 most clearly and grammatically, one ought to say "three pounds fifty," or, for $3.50, it should be "three dollars and fifty cents."

Consider the pronunciation of "three fifty". Is there more stress on the "three" than on the "fifty"? If so, you're dealing with a word compound, and there can be a hyphen. If not, "three fifty" is a phrase not a word, so stress should come at the end.

"Fifty" has more stress than "three", so no hyphen.