The passage of time in Farscape is a bit unclear, but the best that I can come up with is less than a year.
The general rule appears to be that each season of Farscape lasts 1 year:
- It is firmly-established in the Season 4 finale that it was 4 years between the start of the series and the end of Season 4.
- In the Season 4 finale, John says that he flipped a coin with Aeryn a year prior. This previous coin flip occurred in Season 3 finale which means that at the end of Season 3 it had been 3 years since the Farscape-1 mission, and that Season 4 takes place over the span of a year.
- In S03E13, Pilot tells John that they had known each other for approximately 2 and a half cycles. It is stated in S01E11 that one cycle is roughly one year.
- In S03E08, Aeryn says that she has known John for over 2 cycles.
- In S02E20, it is stated that John hasn't used a Tavlek gauntlet in over a cycle. The last time that we saw John use a gauntlet on-screen was in S01E04 so the latter part of Season 2 occurs at least 1 year but no more than 2 years after the Farscape-1 mission.
So if you accept that a year passes between the first and last episodes of Season 3, then the best that you can accurately guess is less than a year because there do not appear to be any additional clues as to how much time is passing throughout Season 3.
Now, if you assume that the time progresses uniformly throughout the season, the duration of the 12-episode arc where Crichton is duplicated could be narrowed down to approximately 6 months in the 22-episode season, but there does not appear to be any definite in-universe data supporting that assumption.