The stretch I use outside of the gym is to bring my humerus up into flexion to about 90degrees, maybe a little higher, with my elbow relxed in full flexion. Then slide the other arm underneath and hold my hand. The lower arm pulls the stretch-arm down at the hand/wrist towards the shoulder, as the weight of the barbell would in the clean, while simultaneously cranking the stretch-arm up at the elbow if it needs any further elevation.
Also look at scapular flexibility, particularly looking at muscles such as teres major and minor, which pull the humerus down onto the scapula, and muscles such as levator scapula and rhomboids, which rotate the scapula in towards the spine. Any tightness in these muscles could prevent you from getting into the proper position at the end.
I also have trouble with getting my elbows all the way up, so I know the dilemma. I find that I can get them up, just not fast enough, so I think for me it's just a movement pattern that I need to work on. If you find that you can get into the rack position without problems when you're not cleaning the weight, then it might also be a motor pattern for you. If not, refer to flexibility recommendations.