Yes a flail is the appropriate gear.
But don't be too hasty to decimate all your rushes. (They're not reeds, they're rushes.)
Rushes colonise wet ground and, properly controlled, can in fact make it more useful. Eradicate them and you may have a useless mudbath half the year. Manage them and they are shelter for livestock (especially sheep and most especially lambs); the fresh shoots are decent eating; the grass which grows in the gaps is often the best grass in the field; and if it appeals to you to support ground-nesting birds, then a mosaic of rushes of varying ages and heights, with some open patches in between, can attract birds such as curlew, snipe, lapwing and grouse (to name but a few) to nest and rear young there.
If you like the sound of all that, then the recipe is to top approx 1/3 each year in disorganised patterns, after the fledglings have left (so not before mid July) and again 6-8 weeks later (if it's not too wet by then to go a-topping :/) Aim to have some clearings but with cover (ie., rushes!) nearby, and a patchwork of younger, smaller plants and more established ones.
You can usually find lots of info about managing rushes for wild birds on the RSPB website, and anything which is good for birds makes good sheltered grazing for sheep
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We tend to let the rushes have the wettest sections of our fields with a few patches on the drier areas so that there is still somewhere for the sheep to shelter even when the wetter areas are completely awash. This year we have been able to keep one such field closed up, nothing grazing in there, since December, and a curlew has recently been sighted flying around...