What phase of matter has enough kinetic energy to partially overcome the intermolecular attraction between the particles, allowing the particles to flow and take the shape and volume of whatever container the sample is in?

The answer is; liquid phase

The characteristics described in the question are those of a liquid. The forces between liquid particles are weaker than the forces between solid particles because the particles are further apart. The particles are not held in a  fixed position in the structure hence it can flow and take the shape of the container in which it is in.

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