Declined same flexible working other staff do

[Notmorewashing]

I verbally asked my manager a week ago for flexible working, 4 hours off every 3 weeks and this was declined.

Other staff doing same job in other depts that are “less demanding” have it approved.

Should I still put in writing? Feel I maybe should have put in writing first.

Yes do put it in writing. Apart from anything else that will force your employer to consider what business reasons there are to refuse it. You'll probably get the same result but you may not and you certainly don't lose anything.