String(describing: key). win1251Encoded и строка ниже лишний пробел.
curl 'https://bill.SERVER.ru/?mod=tick&act=editticket&show=noheader&tickid=128056' -H 'Connection: keep-alive' -H 'Cache-Control: max-age=0' -H 'Origin: https://bill.SERVER.ru' -H 'Upgrade-Insecure-Requests: 1' -H 'Content-Type: application/x-www-form-urlencoded' -H 'User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10_13_5) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/67.0.3396.99 Safari/537.36' -H 'Accept: text/html,application/xhtml+xml,application/xml;q=0.9,image/webp,image/apng,*/*;q=0.8' -H 'Referer: https://bill.SERVER.ru/?mod=tick&act=editticket&show=noheader&tickid=128056' -H 'Accept-Encoding: gzip, deflate, br' -H 'Accept-Language: en-GB,en-US;q=0.9,en;q=0.8,ru;q=0.7' -H 'Cookie: PHPSESSID=075339-SECRET-c3e0e3a02' --data 'clearid=%C0%ED%F2%EE%ED&equipmentid=&objectid=&resolv_date=&ticketgroup=11&resolv_adm=38&newticktext=%F2%E5%F1%F2&save=%D1%EE%F5%F0%E0%ED%E8%F2%FC+%E8%E7%EC%E5%ED%E5%ED%E8%FF' --compressed<meta http-equiv="Content-Type" content="text/html; charset=windows-1251"><form method="POST" name="editticket"></form>
<select name="clearid"><option>Антон</option><option value="4775">=убрать=</option></select>
<textarea style="height:100px; width: 100%;" name="newticktext"></textarea>
<input type="submit" name="save" value="Сохранить изменения">let str = "Проверка"
let cp1251Data = str.data(using: .windowsCP1251)
let parameters = ["comment": cp1251Data]
let headers = ["Content-Type": "application/x-www-form-urlencoded; charset=windows-1251"]
Alamofire.request(url, method: .post, parameters: parameters, encoding: URLEncoding.default, headers: headers)