If you're talking about geometric shapes, both kites (also called deltoids) and rectangles are quadrilaterals and all two-dimensional quadrilaterals are polygons, but a rectangle must have four interior angles of 90º, and a traditional kite shape doesn't meet that qualification.
If all four sides of a kite are equal lengths, then the kite can also be classified as a rhombus.
If both the angles and sides are equal, the kite becomes a square. The only way for a square to have four equal angles is if the angles are 90º each, which means a square is also a rectangle. So a kite can be classified as a rectangle, but only if very specific conditions are met.
Most kites are not square or rectangular in shape. In fact, most kites can be defined as a quadrilateral consisting of equal adjacent sides. A kite divided down the long center becomes two right triangles.
The website listed under Related Links, below, includes a kite shape that can be manipulated online. This is a great tool for visualizing the variations of a kite/deltoid.
(If you're talking about flying kites, they come in a variety of shapes and sizes, some of which may be rectangular.)