The double bar frame is very robust usually, so that much is probably fine.
The big part to locate would be a matching fork. If it's a standard Chinese mail color, you might very well be able to find one. I think you'd have to source one through someone with connections in China. A black fork is easier to find, but maybe someone over there can get a matching/standard color green one if the mail bikes use it.
After that, it looks to me like stuff you should be able to fix or find if you have a connection in China that can send you the parts. Handlebars can be found there, but you might be able to straighten those. If the rod brakes were having issues, a bent set of bars (if bad enough) can cause it. Rims are available still from Chinese or Indian (or British) sources. A single speed free wheel or coaster hub would be OK. Most of these bikes are single speed anyway.
Chrome parts, I'd throw them in oxalic acid and clean them up as best as can be done. A little rust on a working Flying Pigeon is to be expected anyway.
The parts themselves in China are probably quite cheap and plentiful. You just need to get a connection to locate what you need. The Flying Pigeon is somewhat notorious for not matching British or US market type parts.
These bikes have moved more people more miles than any other bike model ever made - cheap transportation in a very populous country. They are kind of going by the wayside now that more people have modern bikes, scooters, and cars there (they love Buicks for some reason).
