I think I get what you mean. Looking at the map it appears as though East Putney is slightly further from West Brompton than Clapham Junction. Trial and error on the fare finder says that you can travel from Canning Town via Stratford, Willesden Junction and West Brompton for the £1.60 off-peak fare, so I think that’s going to be the longest.
Interestingly this has shown up some errors in the data which probably date back to the creation of the zone 2/3 sausage around Stratford. All the stations from East India or Pudding Mill Lane round to Lewisham DLR also offer the option to travel via Stratford, but they all charge £1.70 off-peak because they think you go into zone 3. I seriously doubt anyone would use that route to get from Lewisham to Putney when you can travel via Denmark Hill for the NR zone 2 fare of £2.40 off-peak in considerably less time.