This paper presents asp-fzn, a solver for Constrained Answer Set Programming (CASP) with linear constraints. asp-fzn transforms CASP programs into the solver-independent FlatZinc language, which supports several constrained programming and integer programming backend solvers. It supports a wide range of linear constraints and some general global constraints, and demonstrates competitive performance with state-of-the-art ASP solvers on benchmarks from existing ASP competitions. Furthermore, we evaluate asp-fzn on several CASP problems from the literature and compare its performance with clingcon, a leading CASP solver that supports most of the asp-fzn language. Asp-fzn is competitive on general ASP and shows promising performance, outperforming clingcon on some CASP benchmarks.