How do I progress Farkas' companion story line?

You need to complete the Entire Companion questline to get him as a Marriage option, these include:

  • Take Up Arms
  • Proving Honor
  • The Silver Hand
  • Blood's Honor
  • Purity of Revenge
  • Glory of the Dead

If the quest is bugged it can have a plethora of reasons(mainly due to the repeatable quests).

Options are:

  • Sleep for a day or 2, it might fix itself
  • save, attack the companions and then either sheave your weapon or reload and it might reset.
  • Some quests are wrongfully categorizes, some other miscellaneous quests might block it and need to be completed first
  • Try everybody there might be a single one that does give a job but think u already tried that.
  • Bounties might cause the issue, try paying them al off or getting one and then paying it off

IF that doesn't work your last option is using console commands.