Bakelite oil lamp, never seen.
If the lamp is, errm, oily, you might want to begin with a wipeover of meths.
When I've rescued old switches and sockets, I've used Autosol.
One application.
If there are creases or detail, apply with [someone else's] toothbrush.
Shines up nicely.
Other chrome polishes are available.
After that just ask the parlourmaid to clean with the usual feather duster.
it's an Aladdin oil lamp - apparently not many Bakelite were made, most were metal. No creases or detail nicely plain and to my liking. Not oily either, and I've giving it a nice hot soapy water wash and taken the grime off. It's just dull. The mantle is gone and there is no wick.
The parts you need are easily obtained. The internet and EBay, and other sites have every thing you need. If not here is the link to the Aladdin site. I see you have the flame spreader as well, those can sometimes be a bugger to find at a reasonable price.
http://www.aladdin-us.com/
Ron