The phrase 'take another flight' is correct and can be used in written English.
It is used to suggest an alternative action to the current situation. For example, "If the flight to Tokyo is full, you can take another flight to Osaka."
Don't you know it, I missed my plane, which meant I had to take another flight that stopped in Chicago and disturbed my sleep?
An officer eventually told Opebiyi that he was in the clear but that the pilot had said he should take another flight.
As we were boarding our flight, there was an announcement that the flight was overbooked and calling for volunteers to take another flight in exchange for a financial reward.
Guram Dzhinikashivili, 52, said that for his wife to visit her mother in Kaspi, Georgia — an easy two-hour drive — she was forced to fly to Yerevan, the capital of Armenia, then take another flight to Tbilisi, then drive north from there.
I would have to fly to Detroit, take another flight to Traverse City, rent a car, drive an hour and a half, give a reading, sign some books, get back in the rental car and do the whole thing in reverse.
They took another flight on Friday morning.
Startac, the Turf Paradise Derby winner, took another flight, arrived safely and appears happy to be here.
The man and woman were on the Korean Air flight Sunday from Baghdad, the Iraqi capital, to Abu Dhabi, where they disembarked and took another flight to Bahrain.
Besides, she was taking another flight, so on the off chance that there are the fates, I was sure they would be kinder to her than to me.
After the plane went down, 16 minutes after takeoff, they took another flight back to Trinidad, where they were arrested the next day on a tip from the Venezuelan police.
