The chairman of a council has few rights over and above individual members. Decisions must be made by the council in a properly convened meeting and councillors can insist on having items on the agenda. Although the chairman can call meetings, two ordinary councillors can demand to have a meeting if the chairman refuses to call one. So, provided you can find another councillor to cooperate, you can force a meeting to discuss the matters you feel need attention.
Alternatively, you can simply take action using your status as a councillor. Bigger authorities are not guaranteed to take much notice of parish councils at the best of times, and are just as likely to react to a vigorous councillor as to a whole council. Especially with judicious use of the local press, for example releasing copies of any particularly important letters you write. Also, look for allies among members of the larger councils.
Ideally, councils pull together, but if that isn't working, then like minded councillors can pool their resources towards achieving their aims. Maybe if you start making a noise, you'll spur others into action.
I'm sorry you're flooded, and hope you can get useful support from the bigger authorities.
