If you want to isolate amylase at home, it could be done. However, you'll get all of the other enzymes too, if that matters to you. The key would be keeping everything cold. While amylases are very stable, as soon as you mix in your buffer to start the extraction, you'll also start to get starch conversion, which it sounds like you don't want. If you can keep it cold (as close to 32F as possible you won't get much conversion. If you can keep it cold you could just treat it very similar to a regular mash, then just drain it off and use it to mash in the oats.
Things to do different - besides keeping it ice cold (frozen bottles of water)
Grind as fine as possible to get maximal extraction. However, as you won't be getting starch conversion it is going to stick like a bugger, so add rice hulls. I use a centrifuge in the lab.
You could let it settle and then scoop off the top and pour it through a colander instead. Depending on how much starch you want to let through, you might do this twice, the second time add some cheesecloth to filter out more debris. Or you could put the grain in a 5 gal paint bag and then after your 15 min. lift it out and let it drain and then squeeze it. I actually have done this with plant protein extracts. I do my extraction in a beaker (on ice) and then pour it into a funnel lined with a filter cloth. After it is finished draining, I squeeze it. Just watch out so you don't split the filter bag.
15 min. of enzyme extraction is probably enough. Stir frequently
Some buffer pH 5.2 might help as a stabilizer. In the lab I always use a buffer