Simply Google it. And you'll find that flushing a hydraulic system ranges from insane care and specialty tools like a power flushing setup designed to cause turbulence to scrub the walls of everything, complete disassembly and cleaning by hand, or simply just draining it, break the lines and drain them, and clean the filter screen and replace the filters. It might not even have a filter, so you could add one if you wanted. If i were you i would run it and get it hot, then drain everything you can, including the hoses. Then you can clean screens and replace filters, then fill with some cheap fluid and run it awhile. After awhile check what it looks like, and maybe repeat. If something isn't working right maybe tear that component down and manually clean it, replacing everything that needs it, especially the seals and o rings.
You can see that the hydraulic system isn't that complex, and that since that's the case i would personally be inclined to run it and make some money with it. If something goes south you should be able to repair it without too much trouble, and so i would do a basic flush and then start running the crap out of it. If the tank is rusted and full of crap you can pull it and clean it, some clean larger gravel and soapy water or diesel in the tank, then you shake it which cleans a surprising amount of crap and rust out. Then you can coat it with products designed for that and you're good to go again. You know you have moisture in the hydraulic system because it looks like milk, so drain it and get new in there, then start using it and see what you got. It could be a problem, it could be condensation from sitting so long, machines don't like to sit. My .02.
You can see that the hydraulic system isn't that complex, and that since that's the case i would personally be inclined to run it and make some money with it. If something goes south you should be able to repair it without too much trouble, and so i would do a basic flush and then start running the crap out of it. If the tank is rusted and full of crap you can pull it and clean it, some clean larger gravel and soapy water or diesel in the tank, then you shake it which cleans a surprising amount of crap and rust out. Then you can coat it with products designed for that and you're good to go again. You know you have moisture in the hydraulic system because it looks like milk, so drain it and get new in there, then start using it and see what you got. It could be a problem, it could be condensation from sitting so long, machines don't like to sit. My .02.