The SVD is necessarily an iterative process, therefore no exact flop formula is possible. It also depends on which singular vectors are required. Some approximations given in Matrix Computations, 3rd ed., Golub & Van Loan, page 254 are
- singular values only, 4mn^2 - 4n^3/3
- singular values and some singular vectors U (m x n) and V (n x n), 14mn^2 + 8n^3
An exact flop count would require instrumenting the code, e.g., with PAPI.