It comes as an amber weather warning for rain was put in place by the Met Office as Storm Christoph looks set to batter the city.
Barnsdale Road, in the east Leeds village of Allerton Bywater, near Castelford, has closed due to the flooding.
The video shows cars struggling to drive though the high flood water.
The Environment Agency said the spillway at Allerton Ings is operating but the washlands are filling.
It expects the spillway to continue until Thursday, January 21.
The Government agency said: "River levels are rising as a result of the heavy and persistent rainfall associated with Storm Christoph. Barnsdale Road has flooded.
"We expect the spillway to continue to operate until Thursday lunchtime. We are closely monitoring the situation.
"Please avoid using low-lying footpaths and roads near watercourses, and plan driving routes to avoid low-lying land that may be flooded."
Other parts of Leeds began flooding earlier in the day, with flood alerts in place across the city.
There is a flood alert in force currently for the lower River Wharfe area with flooding of low-lying land and roads possible.
The river has already begun to overflow into a children's playground and a skate park in Otley in Wharfemeadows Park on Farnley Lane.
Pictures, taken at around 8:30am, show the water flooding into the parks from the river.
Local resident Karen Weir lives a two minute walk from the river up a slight hill, so is hoping her home should be safe.
She added: "Luckily we don't flood up the hill on Prince Henry Road but people below the hill on Farnley Lane and Bridge Avenue often do.
"They are quite well prepared though these days.
"There is an Otley Flood Team but they can't go out due to lockdown so builders have provided sand bags for people who need them.
"There's a good community here in Otley and people rally round to help each other."
What to expect in Leeds, according to the Met Office:
Homes and businesses are likely to be flooded, causing damage to some buildings
Fast flowing or deep floodwater is likely, causing danger to life
Delays and some cancellations to train and bus services are likely
Spray and flooding probably leading to difficult driving conditions and some road closures
A good chance some communities cut off by flooded roads
Power cuts and loss of other services to some homes and businesses likely