What are the most similar Earth analogues to Mars' seasonally recurring slope linea?
Analogues to Mars Recurring Slope Linea (RSL) is a current study topic in  Antarctica (Dry Valleys). On Earth, analogues are known as water tracks, which are linear zones of higher moisture along slopes in polar regions where water transit during snowmelt. This figure from Ward Hunt Island (NU, Canada) show well developed and typical water tracks.

Source:  Water tracks in the High Arctic: a hydrological network dominated by rapid subsurface flow through patterned ground Michel Paquette et al. Arctic Science, 2017, 3:334-353, https://doi.org/10.1139/as-2016-0014

On Earth, as shown on this picture from Ward Hunt Island, water tracks are from snowmelt and thus not from brine, unlike in Antarctica where brine water as runoff is common.


  Water tracks share many morphological and seasonal characteristics with RSL, including downslope propagation of linear or branching patterns of surface darkening, growth during spring/summer seasons, and fading during winter


and


  Saline fluids associated with water track flow are sourced by snowmelt, shallow ground ice melt, and the direct conversion of atmospheric water vapor into brines through high-elevation salt deliquescence


from Joseph Levy, Hydrological characteristics of recurrent slope lineae on Mars: Evidence for liquid flow through regolith and comparisons with Antarctic terrestrial analogs, Icarus, Volume 219, Issue 1, 2012, Pages 1-4

This mean that this Antarctica analogue to Mars RSL have several sources of water (meltwater, shallow ground ice and atmospheric water vapor deliquescence).

Comparatively, on Mars, source for the RSL have been hypothesized to originate from snow melting, deliquescence, dry flow or shallow groundwater. And more recently, from deep aquifers  through fractures (impact, tectonic) such as shown in this study at Palikir Crater inside Newton Crater Basin and Triolet Crater. 

Nevertheless, there is entire sessions at the Lunar and Planetary Science Conference dedicated at Martian Brines (MARTIAN BRINES:  OLD SALTS AND NEW VIEWS) and RSL or actual slope processes (THING FALL DOWN GO BOOM:  MARS DOWNSLOPE MOTION). While models are getting better and more elaborated, there is still opposing views and this dynamic field of study is moving very rapidly.

Finally, life found in brine on earth are halophiles, a type of extremophiles - but this is a whole topic in itself.