Take the rubber hoses( nothing wrong with them between the lines and radiator ) off from the rad.
Have a helper position them ( or get longer ones) unto a bucket. e
Start the engine and look for flow from one of the lines.
Then blow air low pressure ( human lung pressure should be enough) in the other.
The supply when the engine is running has pressure, the return should be open to the trans body ( aka atmosphere)
You did not explain the circumstances under which the puking happens ( immediately on startup, after warm up, after hard driving, after interstate driving, around town driving????)
If it's immediately on startup and you get flow and no restriction in the lines to / from the trans you could hook the to together and start it up. If it still pukes then IMHO it's grisly over full, or some other cause I have never heard of.
If it happens at any other time get a known good trans cooler and put it in place of the stock cooler and test.
You can also test the stock cooler with low pressure air for flow.
Another question....
Is the puked fluid foam or liquid?
If it's foam you might have an air leak in the suction side of the system (low fluid, filter not sealing to the valve body, deep pan without the corresponding extension. Leak somewhere else on the suction side). Foamed up fluid expands a lot
