If the universe is flat how can it contain 3D objects like planets and galaxies

The people who say the universe is flat (or incredibly close to it) are called "cosmologists," but they don't mean that it's two-dimensional. They mean that its space-time is not very curved overall: that triangles drawn on it include 180 degrees worth of angle, that the area of circles in it is pi*r^2, etc.

The "flatness" scientists refer to with respect to the universe pertain to its curvature along a hyperspatial axis.

A sheet of paper lying on a table and a sheet of paper rolled into a cylinder are both two-dimensional (I know they're not *really*, just imagine they are), but one is flat, and the other isn't, because one is curved in a higher dimension. The universe is analagous, just one dimension higher. It's a hypersphere, a three-dimensional surface volume of space embedded in a four-dimensional Euclidean hyperspace.

No matter WHAT shape the Universe may be, spherical (positively curved), negatively curved, (hyperbolic), , a combination of of positive and negatively curved spaces (saddle-shaped), OR 'flat" , it has AT LEAST 3 spatial dimensions and one temporal dimension at many different scales of size, from the quantum, subatomic level to the cosmological scale of the entire Universe. When a scientist says the universe is "flat" they DO NOT mean it mathematically "flat" They just mean that the Universe's shape may be like a solid cube or rectangle that is expanding in size. Mathematically and logically, there can be an infinite number of dimensions.

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Cosmologically 'Flat' refers to the 'Shape of Space', and as they
use it, it means that parallel lines are measured to really be so.
it's one of the mysteries of Cosmology, as if the Universe is expanding,
(as we see it to be), this shouldn't be so..