Use a current sense transformer to step-up for a photoflash capacitor charger?
The LT3484 is quite clear in the data sheet: -



The primary inductance is recommended to be about 10 uH. Take note!

The current sense transformer you have highlighted has a primary inductance of at least 80 uH and ranges up to 8 mH depending on which one you choose. The specific one in your question has a primary inductance of 180 uH.

Now you might get it to work very badly with the output capacitor charging slowly and maybe not reaching full expected voltage but if you read LTI's data sheet they specify these parts: -


KIJIMA MUSEN PART# SBL-5.6-1, LPRI = 10µH, N = 10.2
TDK LDT565630T-003 LPRI = 10.5µH, N = 10.2
TDK PART# LDT565630T-001, LPRI = 6µH, N = 10.4
TDK PART# LDT565630T-002, LPRI = 14.5µH, N = 10.2


.... In the example circuits provided.