This is contained in Michors book "Manifolds of differentiable mappings" (available online here 1). It is a bit hidden (see p. 35 under point 4., the relevant result for scalar multiplication is 4.4.3 earlier), since Michor wants to discuss suitable topologies on all smooth maps not only on the compactly supported functions. Michor constructs the Whitney topology via jet bundles.
A description of the topology in local charts can be found in 2, the topological vector space property is established in Proposition 4.3. By the way: a detailed proof establishing the folklore fact that the local charts approach and the jet bundle approach yield equivalent topologies can be found in appendix C of loc.cit..