Is it possible to walk in a friction-less world?
If there is no friction, you can still move by conservation of momentum. Take some stuff with you that you don't need. Throw it away in the opposite of the direction you want to go!
Although friction is not one of the four basic forces of nature, it exists because those basic forces exist. Friction is the resistance to motion of two objects held against each other.
Friction that allows us to walk depends on gravity to convert our mass to weight which holds our feet against the surface where static friction enables the soles of our shoes to push off against the surface of the Earth.
Even when ice skating, kinetic friction keeps the blades sliding against the ice in a forward direction, and static friction allows the skates to push off to propel the skater forward.
Some friction is caused by molecular attraction, such as when Vibram soles are able to maintain grip on smooth rock. This is the result of electromagnetic forces in the rubber molecules of Vibram attracting rock molecules.
Even a rocket engine, which otherwise could be used to propel you in a frictionless environment, depends on the difference in force between friction caused by great pressure of propellant exhaust on a small area (exit pressure) and the lesser friction of propellant exhaust flowing through a larger area (free stream pressure). The equation for rocket thrust shows this:
$$\text{rocket thrust} = \text{mass flow rate} \times \text{exit velocity} + (\text{exit pressure} - \text{free stream pressure}) \times \text{exit area}$$
The coefficient of friction is a measure of how strongly two surfaces will stick together. It's the ratio between the force necessary to induce sliding, and the pressure holding the two surfaces together. It can be used to calculate the amount of friction:
$$F = u \times N$$
$F$ is the frictional force
$u$ is the coefficient of friction
$N$ is the normal force (perpendicular to both surfaces, which presses them together)
If surfaces could slide with no force at all, the numerator of their coefficient of friction would be zero, the coefficient itself would be zero, and the frictional force between those two surfaces would be zero. Here is a list of coefficients of friction of various materials. The maximum coefficient of friction is one, and the minimum is zero.
Friction exists everywhere in the Universe. To have no friction, there would have to be no gravity, no electromagnetic force, no gluons to hold atomic nuclei together, and no bosons to allow the buildup of heavy nuclei in stars. All would be chaos. Newton's third law would be inoperative. The universe would be a soup of uniform density with no structure. Entropy would tend to be maximal. You would not be able to walk.
I assume by zero friction you mean no roughness or deformity in the ground. Perfectly smooth. Even so there is a way to walk. As you plunge your foot into the ground you compress it a little based on the atomic theory of matter. This impression allows your foot to be slightly lower than adjacent atoms and can therefore push away from them. On ice this results in melting the top layers of atoms resulting in the slippery experience we have. In sand you would easily be able to walk as you dig in with each step.