Good grief!
Don't panic. The statutory guidelines obviously overrule an internal procedure so you should look at them not the procedure you have been told to use.
I would sit tight for the minute. If your appeal about your flexible working request fails, you would then bring a grievance and you have PLENTY to put in it, not following several statutory procedures even if we leave aside whether the refusal was justified or not.
Of course you don't want to have to go there, but it's reassuring to know you have so many clear cut breaches to put in, makes it less subjective.
You have the guidelines about what the statutory response to an appeal is. Once it's been more than 14 days without you receiving acknowledgement and invitation to a meeting, I would write to the HR Director again, pointing out that you appealed the decision following the grievance procedure as you were advised to do by [name of crappy HR Advisor], it has been [number] of days since and you have not received an invitation to a meeting which you understand contravenes the statutory procedure for appealing refusal of flexible working requests.
Remember that the 14 days they have to respond is from when they receive the appeal notification, so check when that was - obviously if it was email you will know, if a letter, you may have to allow a few extra days. You will be able to double check if necessary as whoever opens the post there would (should) be stamping it with the date once opened.
You are not jinxed, they are just unbelievably incompetent I'm afraid. I mean really, following the statutory timescales isn't rocket science!
Give them a couple of days after the statutory time limit, then write as I have outlined, with a copy on email as well.