I get the feeling that something good is going to happen.
何か - something
いいこと - something good
起きる - to happen, to occur
予感がする - to have a feeling / to have a hunch
何かいいことが起きるような予感がする - I get the feeling that something good is going to happen. もしくは I have a feeling that something good is going to happen.
虹を見て、何かいいことが起きるような予感がした - When I saw the rainbow, I got the feeling that something good was going to happen.