By definition, fixed overheads in total do not change with the level of production and therefore in a flexed budget the fixed overheads will stay the same.
I think you are confusing it with the fact that if we are using absorption costing then it effectively treats the fixed overheads as though they do change with the level of production – that is why when producing an absorption costing profit statement we then need to adjust for any over or under absorption of fixed overheads (as in my lectures on absorption costing) and why when calculating variances using absorption costing the fixed overhead variance is analysed into expenditure and volume variances (as explained in my lectures on variances).