A siphonic flush toilet system and method of priming the same having a toilet bowl assembly comprising at least one jet flush valve assembly and at least one rim valve; and bowl having a rim and a jet defining at least one jet channel. The bowl has a closed jet pathway to maintain the jet channel in a primed state with fluid from the jet flush valve assembly to prevent air from entering the closed jet pathway. Flush valves may have back-flow preventer mechanisms and/or at least partly flexible valve covers, including specific valve cover structures. Flush activation assemblies may have a flush activation bar connected to the pivot rod and/or an adjustable flush connector located between the pivot rod and the flush activation bar. A kit providing one or more flush activation elements is included. The kit elements may be usable with the toilet systems and methods described.