For last 3 weeks I am using diesel for my cleaning and lubing my bicycle chain, so far I am not facing any problems.
Should I continue this or am I damaging my chains ?
Has anyone else using this method ?
3 weeks isn't likely enough for you to damage the chain noticeably (rattling sounds and all that jazz) unless you're putting particularly heavy mileage.
This isn't something I'd recommend doing; diesel fuel doesn't have the right lubricating properties for a bicycle chain. It's also not the most pleasant stuff to be around.
Diesel will act as a degreaser which will clean the chain, but this is against most chain manufacturer's recommendations to begin with (which I've outlined here).
I'd suggest following the directions of the manufacturer and using a bicycle specific chain lube (or 3-in-1 if you want to save money), and a damp cloth to periodically wipe down the chain after riding and re-lubricating. I do own a chain washing machine, but it hasn't been used in quite a while.