System open to air for months to decades then likely can a lot more problems then a flush will help.
Evaporator and other parts likely "rust" inside and on them and may not have a hole now, rust damage makes them weak and fails soon after you spend money to replace missing parts at minimum.
All "rubber" parts are likely dead too.
Many Real AC shops won't touch this no matter the cost because can't guaranty will work for even a day or two. And that's even If
the old compressor did not
have "Black Death" and other things blowing crap thru the system. acc/drier can fail and blow desiccant causing compressor fail as well.
DIY cost at minimum cost for...
Compressor and likely mounting hardware.
Likely need to replace crank pulley for rust damage.
Acc/Drier... Ignoring your issue for the moment, New and Rebuilt Warranty Require this on all system.
All New hoses not just missing ones.
All seals valves and many electric parts. Electrical?
At minimum, Clutch switch plus New limit switches need new plugs for them.
Plus Many hours to fix/flush/replace etc.
Then hope doesn't fail again soon.
Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
The Ogre's Fiero Cave