Check out my iNat profile for installation instructions and examples of a beta R package that can handle this request: https://www.inaturalist.org/people/hanly
Once installed, the following code will get you what you want (including combining all pages of JSON data) into a single data frame as long as the request doesn’t exceed 10,000 records:
df <- iNat(taxon_id = [insert the number here], quality_grade = "research", term_id= 12 , term_value_id = 13)
For example this would be Yellow Coneflower:
df <- iNat(taxon_id = 85332, quality_grade = "research", term_id= 12 , term_value_id = 13)
which recreates in a data frame the two flowering RG records seen here:
https://www.inaturalist.org/observations/identify?quality_grade=research&term_id=12&term_value_id=13&taxon_id=85332&place_id=any
This gives you a data frame with 138 column variables that you can inspect with colnames(df) since likely you won’t need most of them.