The university I'm going to get my engineering degree at just eliminated it's nuclear engineering program and absorbed it into a different program (applied mathematics and physics). It still has other engineering programs.
Can you still get a job as a nuclear engineer if you have only a chemical engineering and mathematics degree undergrad?
Any physics based major should be alright. There will definitely be nuclear modules and you'll learn the core of what you need. You can always transfer or do further study later.
There are very few specific NEng programs worldwide but obviously the demand is huge, so naturally most are going to be coming from other relevant courses.
Depends on the country, engineering is one of those fields where you need to be a certain type of engineer to do certain things. In the united states, you might be able to get hired at a nuclear plant, but you degree would likely limit what you can do. A great deal of universities have consolidated their nuclear engineering department, very few new facilities are being built in the world and with nonproliferation agreements the job market isn't what it once was in the 70's and 80's. Chemical Engineering have more crossover with Petrochemical Engineering. Just don't end up doing food science shit, figuring out the best temperature to serve a bigmac is a waste of a qualified engineer.