It's likely you have TWO valve springs and the third item is the valve spring "dampner". A rather flat winding that looks like a spring. Proper breakin prodedure for a flat tappet cam is indeed to remove the inner round wire spring. Run the engine for 2o to 30 minutes at varying rpm never below 2000 or so. Vary the rpm some so that different parts of the cam get "splashed" during the break in. Re-install the inner most spring after breakin.
There is a valve compression "tool" you can buy (fairly cheap), which is what I used to do mine. Depending on your type of valve you may need to "fabricate" something in addition to work or use with the valve tool. Here is a picture showing one possible way to do it. I used an old rocker arm shaft and an actual valve tool. The picture just demonstrates another possible way.
VERY important: You'll need an air compressor and will have to fabricate or buy an adaptor to fill the cylinder with air pressure. This will hold the valve firmly in place while you depress the springs to remove the keepers. I like to bring the cylinder up to TDC before I apply the air pressure. No air pressure will result in the motor "swallowing" the valve!
More information on my "Engine Blog" thread:
427 side oiler engine build "Blog"