It's not going to be a long stroll.
Will you have a car already when you are in Vernazza? If not, then just take the train to Florence.
If you intend to go to Vernazza by car, it's a very narrow winding road to get there. Parking might be an issue too. You might be better off parking in Monterosso then go to Vernazza by train. However the best option is not to have a car at all for that area.
If you insist on the car, the easiest way to Florence is to drive from Vernazza to Levanto and from Levanto to the A12 freeway. Then follow the directions to Livorno. As you approach Viareggio, take the directions to Lucca-Firenze. That will put you on a freeway that connects you to the A11. Proceed to Firenze (Florence). The A11 ends next to the Florence airport. From there it depends on where you need to go. Return the car? Hotel? Apartment?
The drive from Vernazza is maybe 2.5 hours. There are no problems if you know how to drive on narrow curvy roads and if your accommodations in Florence is accessible by car (i.e. outside the ZTL). Also street parking in Florence is scarce .