Make sure you communicate clearly with your employer all the way through the process and keep a good record. The law says that if your employer arranges a meeting to discuss your request or any appeal, and you fail to attend this and one more rearranged meeting without 'good reason', the employer can treat your application as withdrawn.
You have no statutory right to be accompanied to the meeting to discuss your flexible working application by a union rep or a companion. However, your union may have negotiated improved rights to representation at your workplace. Check the position with your rep.
Also, if you lodge a grievance, for example, because you believe that your employer engaged in unlawful discrimination when dealing with your request to work flexibly, you have an established statutory right to be accompanied by your rep to that meeting under section 10 of the Employment Rights Act 1999.