Airline safety rules generally require power banks with lithium-ion cells to be carried only in cabin (hand) baggage; putting them in checked luggage is banned by most airlines, since there is no way to respond to a malfunction in the cargo hold.
Capacity limits are usually set in watt-hours (Wh): power banks under 100Wh can typically be carried without extra approval, 100-160Wh usually requires airline approval (and a limited quantity per bag), and anything above 160Wh is banned outright by most carriers.
To convert a capacity listed in mAh to Wh, the rough formula is (mAh × voltage) / 1000. A standard 20,000mAh power bank at a typical 3.7V cell voltage works out to roughly 74Wh, which clears most airline limits without issue.
Charging a phone during a flight is generally allowed, and wired charging still works even with 'airplane mode' enabled. In-seat USB outlets are often low power, so do not expect fast charging from them; bringing your own power bank is the more reliable way to get real charging speed.
Keeping the power bank in a separate, easily accessible pouch speeds up the airport security check. Charjett's travel-series power banks are designed to stay under these Wh limits, which makes flying with them straightforward.