Troubleshooting
Sounds like you are doing everything correctly. We would apply the Brown to the copper first and wash it off (and highlight it with a Scotch Brite pad and wash it again). While the metal is still wet we would apply the Green Patina with a stiff bristle brush (do not wash it off) let it dry and leave it alone until tomorrow. Re-apply the Green the next day if necessary.
There are two main reasons for the finish flaking off. The first reason would be a problem with how the metal was prepared and cleaned. The more likely (and very common) application error is that the object has been left in the solution for too long. The object should be removed from the solution as soon as the desired color is achieved and washed off well with water. If the metal stays in the solution for longer than that, the finish will just build up on top of itself, have nowhere to go, and easily flake off.
The trouble you are having is most likely caused by surface preparation and/or cleaning. Jax Green Patina only works on clean metal. No oil, lacquer, grease or wax – even fingerprints can be a problem. It may take several different cleaning products to really get down to bare metal. We suggest the use of steel wool or sandpaper in addition to cleaning to really be sure you are on metal. We also suggest Dawn dishwashing liquid and warm water before using the Green Patina. You can apply the Green while the metal is still wet. Apply with a stiff bristle brush and do NOT rinse it off. Remember, the Green does not work instantaneously – apply and then walk away until tomorrow. We would also consider the use of one of the Jax Darkeners (our preference would be Jax Brown-Black) before you apply the Jax Green Patina. It will be far more authentic than just applying the green on top of virgin copper.