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FLASK (Full-sky Lognormal Astro-fields Simulation Kit) makes tomographic realizations on the sphere of an arbitrary number of correlated lognormal or Gaussian random fields; it can create joint simulations of clustering and lensing with sub-per-cent accuracy over relevant angular scales and redshift ranges. It is C++ code parallelized with OpenMP; FLASK generates fast full-sky simulations of cosmological large-scale structure observables such as multiple matter density tracers (galaxies, quasars, dark matter haloes), CMB temperature anisotropies and weak lensing convergence and shear fields. The mutiple fields can be generated tomographically in an arbitrary number of redshift slices and all their statistical properties (including cross-correlations) are determined by the angular power spectra supplied as input and the multivariate lognormal (or Gaussian) distribution assumed for the fields. Effects like redshift space distortions, doppler distortions, magnification biases, evolution and intrinsic aligments can be introduced in the simulations via the input power spectra which must be supplied by the user.