Good question. While I know the area north of the Yare very well, i'm not so familiar with this side of it. I've looked at google maps but it's difficult to work out a walking route because of the marshes.
I wouldn't be surprised if there was no signposting at all from Wickhampton(for the actual station). Might be worth getting hold (or having a look at) an Ordnance Survey map if possible as you could end up with wet feet/going round fields trying to get across dykes if you don't use a footpath.
I reckon it would be walkable though. Maybe 3-4 miles?
It is walkable, as far as I know, although I am not especially familiar with that specific set of footpaths around there. I think the OP would need to walk from the church at Wickhampton and follow the track/road to the right of the church in an Easterly direction until it ends, then turn left (thus heading North-East) onto what appears to be an unnamed (maybe unmarked) footpath. This path meets the Weavers' Way (should be signposted), which heads in two directions, so turn right and head South-East. This leads to the foot crossing at the railway station.
I too would suggest walking distance is around 3-4 miles, not counting any wrong turns which even experienced walkers have made in that area. It may be easier to follow the Weavers' Way from Stone Road, Halvergate (Halvergate is just North of Wickhampton). I would leave plenty of extra time in case of this, plus walking speeds slowed by mud - oh, and the local timetable.
I am going by what local knowledge I have, OS Landranger 134 ("Norwich & The Broads; Great Yarmouth" - unfortunately I only have the 1997 Edition to hand) the Open-Source map at
http://www.openstreetmap.org/#map=16/52.5911/1.5918 and also some local walking maps which I am remembering "off the top of my head". However, I cannot guarantee any accuracy!
Edit: I see since looking this up and posting that 3 other posts have appeared. This all seems good advice to me. I would add that the Weavers' Way is not the exact footpath from Wickhampton so may be slightly harder to access.