Ms Flynn, 24, was reported missing on Monday afternoon after concerns were raised for her welfare when she left her home in Lifthouse, Wakefield.
The car she was driving – a yellow Volkswagen panel van with the registration P97 1MHK – has been seen in Scotland twice since she went missing and officers are appealing for anyone with information to come forward.
Ms Flynn is white, wears glasses and has blonde hair.
The distinctive yellow van was seen on the A1 south of Edinburgh on Tuesday morning, and on the M74 near Abington, South Lanarkshire, later on Tuesday.
West Yorkshire police officers have asked that anyone who has seen Ms Flynn, or has any information on her whereabouts, contact Leeds District CID on 101 quoting incident number 992 of September 13.
Alternatively, you can submit information online here.