i was going to suggest putting a blurry ruler up against the pins and measuring the pitch (pin spacing).
anyhow, it looks sort of like the socket for this.. https://www.amazon.com/HIROSE-ELECTRIC-DF13-6S-1-25C-Position-Single/dp/B073RPP3DQ
Hirose Electric DF13 - 6S-1.25 ° C DF13 Series 6 Position Single Row Pass Through Crimp Socket (HRS, Hirose)
i don't know what the flat-tip spec is called. they have a catalog to look at, website to search