Chickens can fly, but only for short distances and limited heights.
Chickens can fly

FactVerify
Source: factverify.com
Key Evidence
Multiple sources confirm that chickens can fly short distances and heights, with some flights recorded up to about 92 meters in length and around 10 feet in height. Their flight is typically used for escaping danger or reaching elevated roosts rather than long-distance travel.
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What the Evidence Shows
Chickens are capable of flight, but their flying ability is limited compared to many other bird species. Most chickens can fly short distances, typically to escape predators or reach roosting spots. Their flight is usually low and brief, often covering distances under 100 meters and heights around 10 feet.
This limited flight capability is due to their body structure and breeding, which favors heavier bodies and less aerodynamic shapes compared to birds that are strong fliers. Some breeds are better at flying than others, but generally, chickens do not sustain long or high flights. Videos and observational reports confirm chickens flying short distances in yards or farms.
Therefore, the statement that chickens can fly is accurate but requires the context that their flight is short and not sustained.