It seems to depend on what source you read as to when the MLA (medial longitudinal arch) stabilizes, but here is a number, between 7-9 years old.
Conclusions: The MLA of children remained stable from 7 to 9 years old. Gender and the type of footwear worn during childhood may influence MLA development.
Medial Longitudinal Arch Development of Children Aged 7 to 9 Years: A Longitudinal Investigation.Jasper W.K. Tong, Pui W. Kong Journal of American Physical Therapy Assoc. DOI: 10.2522/ptj.20150192 Published February 18, 2016