The OP was asking about an unaccompanied minor:
Flybe customer services informed me earlier today that a 15 year old can travel on their own domestically (In the UK) without photographic id but with a debit card providing they are checked in with an adult at the airport.
CabinCrewe's response relates to an accompanied minor
"Children under the age of 16 do not need to show ID on domestic routes. The adult they are travelling with can vouch for the infant's/child's identification, providing the relevant photo ID is shown (by the adult). "
The relevant bit on the FlyBe website seems to support comments from the Flybe customer services
Rules and regulations for unaccompanied children
To be 'accompanied', the companion of a child must be over 16 years of age.
Identification of the escort on departure & escort on arrival will be checked, and the child signed for, in line with current policy.
If a child is not travelling with their parent or legal guardian, he or she must carry their own identification. If no identification is available please contact us. You will need to send a copy of the photo identification from the parents and confirm that the child is travelling with their consent.
Passengers aged between 12 and 16 years who are not travelling as an unaccompanied child require their own photographic identification.
For passengers on international flights a valid passport or national identity card will need to be presented. Other documentation such as a visa should also be sought if required.