Do I have to accept a flexible working request?

No, but you do have to handle it properly. Flexible working is now a day-one right. People can make two requests in any twelve months, and you have to deal with each one reasonably and give an answer within two months. You can only say no for one of the eight business reasons set out in law, like cost, a hit to quality or performance, or not being able to reorganise the work.

The risk is a gut no without working through it, or turning one person down while letting someone else do the same thing. That's where a refusal turns into a discrimination or grievance claim, especially if the request is tied to childcare, health or a protected characteristic. So consider it properly, meet to talk it over, and write your business reason down clearly.

General guidance to help you decide your next step, not legal advice. Employment law changes, so always check the current position for your own situation.