As Shri said check with your HR first for the housing tax allowance requirements. Most will require proper receipts as well, and chances are if your landlord will not do the stamp duty they won't provide receipts either. No point paying the stamp duty in that case, unless you are going to risk it and make the receipts yourself.
Our landlord lives in public housing (and thinks we don't know), but still does the stamp duty - minus his address of course. He also initially refused to provide receipts, then said he would only provide receipts directly to the company HR. Finally got him to produce receipts and give them to us. Made his name unable to be read without enigma-grade deciphering skills, and of course no address.
Good luck with it all, getting round dodgy landlords requires way too much time and effort. Next time establish these requirements in writing before signing.
Edit: just seen LL will give receipts, so ignore above, except last para, on avoiding dodgy LLs next time.