Unrestricted means you must have permanent leave to remain in the UK. There are four ways to have that: Be a UK citizen, be an EU citizen, be a citizen of an EEA member state, or apply for immigration to the UK under any of the various schemes offered by the Immigration and Nationality Directorate.
I seriously doubt that FlyBe will bother at all helping you with a work permit for several reasons. First, there is enough interest in the UK that they don't need to bother. Second, there isn't enough time since their cadets will start training in April. Third, even if they did help you, it would be quite unlikely you could get a loan from a UK bank to fund the course if you don't have the needed cash.