Flow is when something is moving uninterrupted with a steady consistency. It can be used literally or figuratively. Literal examples would be: "Watching the river flow is very beautiful." "Since the plumber fixed the faucet, the water is flowing nicely." A figurative example would be: "My business is doing really well, money is flowing into my bank account." Ooze is used much less frequently. It is typically used for something that is very slowly moving out of another object. "The blood is oozing out of my cut." "The toothpaste is almost empty, it oozes out of the bottle." "The sap is slowly oozing out of the pine tree." Flow is a much more common word and can be used in many different cases.

Water flows, but oil would ooze. Blood might ooze from a wound.

Yeah, I agree with Chris, To ooze is used for example in a case when you have problems with your plumbing, and water slowly oozes from a pipe or a mixer.