It depends on the context. Largely, I'm finished' is not equal to 'I'm doneready. But if the scene is something like what I will now mention, I'm finished' is understood as 'I'm ready.'
Come on buddy, let's go to movie ~ Sure, but let me complete my homework. Just 10 minutes.
And the friend waits in the room killing time by watching TV.
After 10 minutes...
Jack, I'm finished (with my homework). Let's go
Finished can be used to mean no longer doing something or having thing completed.
People do use this word that way as in here, here and here. See that here, in no example, it means someone is 'ready'.
True, it's used as an adjective and it's quite similar to -I'm done; I'm over with ... etc.