I need to program an EPROM/EEPROM with the code for an 8085. I do not have a programmer. I can't buy one. But I have access to an 8085 kit. Can I use it to program the EPROM/EEPROM via an interface? What difficulties may I expect if I do it this way?
Usually those kits include a monitor program and some kind of battery-backed RAM.
You are going to have to find an instruction manual and read it however, since you will need access to instructions and such like. If you read the manual, then you probably won't need to ask the question, so I guess RTFM (Read The Fine Manual) is the only possible answer.
Here is a typical such board, and the blurb states:
8K bytes of Powerful Monitor Program using 27512 EPROM
8K bytes of RAM using 6264 with Battery Backup using NICD Battery
So if that was the one you had, and you had the manual, you should be able to use the monitor program to load a user program into battery-backed RAM and execute it. The monitor may do some trickery like modifying your code to insert breakpoints for debugging, so do read the manual.