Hi Tarrynki,
Good news and bad news. The good news is that your boyfriend, as a holder of a British passport, won't have to solicit any additional visa to work. He will have plenty of work opportunities once he arrives.
Unfortunately for you, as a non-EU citizen, will have more difficulty securing legal teaching work. Very few academies offer to help with visas of non-EU citizens since there are plenty of EU teachers available. However, if you register at a reputable academy or university for classes (Spanish classes or otherwise) you *may* be eligible for a student visa. Once you have a student visa you will be able to work legally for up to 25 hours/week.
Good luck with your job search!
Rebecca