There is maybe one condition under which such a planet might work: It would need to have a very rapid rotation, as in one hour long days, probably even a lot shorter than that, someone else can do the math, but it would depend on how flat you want your planet to be. And it would need to have a lot of atmosphere.
If it did not have a rapid rotation, then the atmosphere at the equator would most likely be thinner than than at the summit of everest, as all the water and atmosphere would flow off into the poles and create a spherical gas planet that has a large disc of crust in it's centre, basically leaving the equator in the upper atmosphere.
Earth is wider at it's equator because of its rotation, it's not a perfect sphere, and is actually 64km wider around the equator than it is from pole to pole, and as a result of it's rotation, the atmosphere is thicker over the equator and the oceans are deeper because they bulge out due to planetary centrifugal forces. If a planet was rotating rapidly enough as it formed, it might flatten out a bit as well as throw some of that atmosphere out over the equator, and make it livable.
At the poles - the gravity would at least feel much greater because those centrifugal forces wouldn't be present. I don't imagine that the environment would be very hospitable at the poles, I'm guessing that despite the shape of the core and crust, that the planet would still be spherical, and the flat poles would have an immense amount of dense gases over them. The poles would be stormy, dark, and probably toxic.
I'm picturing something like this:
It's basically a gas planet with a squashed earth inside it, and it rotates really fast. I call it "Earth Sandwich".
The real question is, what would make a planet rotate so rapidly?