Most of the existing habitat suitability index (HSI) modeling are related to wildlife, very rarely used in case of plants. It is a simple mathematical expressions for calculating one or more environmental variables, not related to demography and survival of parental and their offsprings. The calculated HSI values typically mapped and analyzed potential distribution and high value indicated more suitable habitat, whereas low value is unsuitable habitat.
HSI does get used more for animals, but I think that, in the UK at least, is because of they are more likely to be protected species and therefore included in the relevant assessments - I can thinkk of no reason why the same approach wouldn't work for plants. If you have the relevant data for the species you are interested in, then you can calculate HSI for them.
In most cases, I would expect you may have to develop your own HSIs, but generating preliminary HSIs for tree species should not be difficult as long as one has some decent preliminary information on distribution. I would expect the most accessible information would be selected climatic and geographic variables, which can be used to generate models on limiting climatic and geographic bounds. I say preliminary because such models would have to be validated to determine whether the particular variables is actually limiting or correlated with another variable or variables that may be the actual limiting one(s). If one is lucky to have other less accessible variables, such as soil moisture, soil temperature, soil pH, and various soil nutrients, these could be modeled as long you have a large enough geographic template upon which to model them. In all cases, consideration of the appropriate y-axis response variable upon which suitability is based is important, but one may have to begin with what is available and iteratively test it for suitability. Perhaps the simplest response variable is some measure of occupancy at a particular scale. Choosing the scale requires avoiding excessively zero-inflated data but having enough zero points to adequately characterize the conditions limiting distribution.
If we consider habitat suitability index as quantitative assessments of habitat relationship, you can find lot of them related to plants, they are usually named as species distribution models, habitat suitability models, ecological niche models. As stated before, you can build your own suitability model if you have species occurrence data related to environmental data likely to influence the distribution of the species. You have several methodological approaches, I usually run Generalized Linear Models in R statistical software using the rms package by F. Harrell (e.g. https://www.researchgate.net/publication/236870185_Modelling_species_distributions_with_penalised_logistic_regressions_A_comparison_with_maximum_entropy_models)
In some regions this kind of models are already fitted for several tree species and habitat suitability maps and/or species response curves can be generated and downloaded from public online resources (e.g. http://www.magrama.gob.es/es/parques-nacionales-oapn/publicaciones/Semillas_-_Anexos_tcm7-320577.pdf, http://www.opengis.uab.es/wms/IdoneitatPI/index.htm, http://spatial.ala.org.au/)
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