I want to know whether Goddess Santoshi is an avatar of Goddess Durga?
Santoshi Mata is a relatively new goddess venerated as 'Mother of Satisfaction'. She emerged as the goddess in early 1960 through word of mouth and fasting culture. However, there is exactly no reference of Santoshi Mata in any Hindu scriptures.
Another important thing to note is that Santoshi Mata only became popular after the 1975 Bollywood movie 'Jai Santoshi Maa'. According to the movie, She was said to be the daughter of Lord Ganesha. The movie showed that Lord Ganesha's sons Kshema and Laabh ask Lord Ganesha for a sister on Raksha Bandhan festival when they see Goddess Mansa tying Rakhi on Lord Ganesha's hands. Below is the extract from wiki article describing the birth of Santoshi Mata as shown in the movie:
The film 'Jai Santoshi Maa' links the birth of Santoshi Mata to the festival of Raksha Bandhan, where a sister ties a rakhi string bracelet on her brother's wrist and the brother gifts his sister sweets, gifts and a promise of protection. When Ganesha's sister Manasa celebrates the festival with him, his sons ask Ganesha to grant them a sister. Although Ganesha initially refuses, upon the repeated pleas of his two wives Riddhi and Siddhi, sons, sister and the divine sage Narada, Ganesha creates Santoshi Mata through two flames rising from his wives' breasts. Narada decreed that this mind-born daughter of Ganesha will always fulfil everyone’s desires and thus, would be called Santoshi Maa, the Mother of Satisfaction.
Since, She is not described in any Hindu scripture therefore it is not sure whether She is an incarnation or not. It is rather doubtful whether She actually existed or not.