Generate binary matrices which are distinct up to reflections
Jelly, 19 bytes

Ṛ€;U;
2ḶṗṗµWÇ³¡Ṃµ€Q


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How it works

2ḶṗṗµWÇ³¡Ṃµ€Q  Main link. Argument: n (integer)

2Ḷ             Unlength 2; yield [0, 1].
  ṗ            Cartesian product; construct all vectors of {0, 1}^n.
   ṗ           Cartesian product; construct all vectors of ({0, 1}^n)^n.
               This yields A, the array of all binary n×n matrices.
    µ     µ€   Begin a new, monadic chain and apply it to all matrices M in A.
     W           Wrap; yield [M].
      Ç³¡        Call the helper link n times, initially with argument [M], then
                 on the previous return value.
         Ṃ       Take the minimum of the results.
               This replaces all matrices with the lexicographical minimum of their
               equivalence classes, mapping equivalent matrices to the same matrix.
            Q  Unique; deduplicate the resulting array of matrices.

Ṛ€;U;          Helper link. Argument: L (array of matrices)

Ṛ€             Reverse the order of the rows of each M in L.
   U           Reverse the order of the columns of each M in L.
  ;            Concatenate the resulting matrix arrays.
    ;          Concatenate the result with L.