The proper way to say it is: 생일이 (몇 월) 며칠이에요? or, as a poorer choice, (몇 월) 며칠이 생일이에요? (몇 월 means what month, and 며칠 what day). In speech, 이 can be dropped, but including it makes the sentence sound better. In English, the only proper order is "When is your birthday?', but Korean is more flexible, so that 생일이 언제예요? and 언제가 생일이에요? are both grammatical. The best way is to put the more important or broader meaning word in the beginning. - 생일이 언제예요? - 생일 sets the topic at the beginning. You go from a broad idea to details. - 언제가 생일이에요? - When you hear 언제, you have less clues as to where the question is going. So we say 이름이 뭐예요? and 직업이 뭐예요? (these sentences are even more strange if you reverse the order) rather than 뭐가 이름/직업이에요. Dates and addresses also go from broad to specific, as in 2020년 7월 17일 and 서울특별시 종로구 XX-동/로 YY (starts with the city).

생일 며칠이에요 이게 맞는 표현입니다.

We don't say 며칠 생일이에요? (it sounds werid) But yes, we say 며칠이 생일이예요?