I looked this up many years ago, as one of my school fire drill's was also treated to a Red Arrows flypast.
You can request a flypast and provided they are in the area/there is a justifiable reason for their participation they will usually do it I think.
EDIT: Found the application form, for those interested: https://www.raf.mod.uk/documents/word/flypast-request-form-2023/