The Gills finished fifth in Stimson's first full season in charge to set up a two-legged semi-final clash with Rochdale and King, who was a big-money signing by previous boss Ronnie Jepson, is enjoying working with the former Stevenage chief.
"He's been great for me since he's come in," he said. "He's one of those managers who lets you go out and play your own game, encourages us to get the ball down and pass and it suits me well.
"I've built up a good working relationship with him."
One of Stimson's innovations was to begin pre-season training in early June last year and King feels the team are showing the benefit of that as the season draws to a close.
"I think it's starting to pay off now," he added. "We look fit through games and especially in the later stages, we keep going and I think that's part and parcel of our fitness work."