What evidence is there for geological mechanisms that formed the Siberian traps flood basalt?
This answer will focus on recent research evidence found within the Siberian Traps deposits.  For the purposes of this answer, the theory that a possible Wilkes Land impact resulted in the Siberian traps as an antipode volcanic response will not be included (please see the question and answer to Can impact events cause widespread volcanic activity on the other side of the planet? for details of current modelling doubts of this mechanism).

Many researchers cite that the initial cause of the Siberian Traps was a mantle plume, some refer to it as a 'superplume' that inpinged into the upper mantle, as shown in the diagram below:



Image source: The Permian Period, Palaeos.

However, according to Sobolev et al. (2011), observations and measurements of the region affected by the Siberian Traps exhibit no evidence of pre-magmatic uplift nor lithospheric stretching that can be associated with mantle plume activity (e.g. the Afar Region in Ethiopia), their models suggest that there was extensive plume erosion of the cratonic crust over a considerable length of time.

Petrological evidence by Sobolev et al. (2011) suggest that some recycled oceanic crust existed at the head of the plume. This contamination was noted in $\delta^{34}\ce{S}$ analysis of melt inclusions by Bryan and Ferrari, (2013) and Black et al. (2014), who determined that the mantle melt source was close to that found in mid-ocean ridge basalts.

Black et al. (2014) also note that a significant contributor to $\delta^{34}\ce{S}$ (up to 25%) was derived from evaporitic sources. This related to the observations made by Jerram et al. (2013) of the contact metamosphism around the doleritic dykes and sills, indicating that the basaltic magma was injected into an organic and salt rich sedimentary basin.  This interaction between the organics an salt and molten rock would have released halocarbons, $\ce{CO2}$ etc that are attributed to the mass extinction at the time (Jerram et al. 2013; Self et al. 2014).

This, and the prevalence of tuff leads to Jerram et al. (2013) questioning whether the Siberian Traps were the result of widespread explosive volcanic activity, related.  The dyke and sill intrusions are believed to have caused episodic explosive eruptive sequences, according to Self et al. (2014).  Some of these eruptions were phreatomagmatic depositing mafic volcaniclasts according to Bryan and Ferrari, (2013).

As, the crust eroded due to the plume (Sobolev et al. 2011), the eruptive sequences transitioned to basaltic lava flows, these are believed to have also been episodic, according to Self et al. (2014) with pulses of magma production and lava eruptions.

The map below shows the distribution of sill intrusions, pyroclasts and lava of the Siberian Traps.



Image source: IAVCEI - the red are sill intrusions, the light purple are pyroclasts and the dark purple is lava.

References

Black et al. 2014, Sulfur isotopic evidence for sources of volatiles in Siberian Traps magmas, Earth and Planetary Science Letters

Bryan and Ferrari, 2013, Large igneous provinces and silicic large
igneous provinces: Progress in our understanding
over the last 25 years, Geological Society of America Bulletin

Jerram et al. 2013, What happened at the start of the Siberian Traps? Understanding the onset of flood volcanism, American Geophysical Union, Fall Meeting 2013

Self et al. 2014, Emplacement characteristics, time scales, and volcanic gas
release rates of continental fl ood basalt eruptions on Earth, The Geological Society of America
Special Paper 505

Sobolev et al. 2011, Linking mantle plumes, large igneous provinces and environmental catastrophes, Nature