I also gave a bit of thought to that route, but it seems
@Trickedem has beaten me to it. That is broadly what I was going to suggest. A couple of observations: Trickedem's route has you going along the busy A229 near Kits Cottage. It's possible to actually go under it via a bridge. Finding the bridge is a bit tricky. You have to go the "wrong way" on a cycle path up the sliproad (Old Chatham Road) probably past lots of parked lorries)
Trickedem's route
View attachment 401147
My variation. I go under the main road via a bridge by the Shell garage
View attachment 401148
Also note that the dotted line that goes off to the right hand edge of the map (to the East) next to the Shell garage is a cycle path. It cuts a big loop out. Note also that I didn't go along it. This is because it's quite muddy and when I tried it I had to walk for a kilometre or so.