Later this year (hopefully) we have a flight on China Eastern. If we check in on line can we go through security with a boarding pass that is printed on our home printer? At this time the flight is still scheduled because it isn't until September 2020.
If the airline will provide you with a boarding pass that you can print on your home printer, you can use it to pass through security. You can also generally display such a pass on a phone or other mobile device.
Source: I've done this several times myself.
However, there can be cases where the airline does not allow online checkin, or for some other reason you cannot get or print or show the pass. In such cases, you can pick up a boarding pass from the checkin kiosk or a ground agent and use that instead.
Source: I've also done this several times myself.
When you enter the line at TSA security you will be asked to scan the QR code on your boarding pass. You can do this from any means at your disposal. Many people use their phones these days. But it's perfectly fine to use a boarding pass printed at home if your airline provides it.
Note that in 2020 TSA is moving toward a new document checking system which will require showing only your ID to TSA; you won't have to also show your boarding pass as their computers will look it up using your ID. Once implemented you will only need the boarding pass at the gate. This system is already being tested in a few airports, but as of this writing JFK is not one of them.
CAUTION. Even if this is allowed by the airline, you may be stopped by TSA if the bar code on your boarding pass is illegible to their reader. (This has happened to me when I relied on a finicky inkjet printer.) When that happens, you will be sent back to the check-in counter to get a new boarding pass. You will then have to stand in two more lines to reach the TSA checkpoint.
Practices vary with airlines and airports. What I've found when flying to China is that there's no problem getting through security on a home-printed or cellphone boarding pass, but while waiting at the gate for the first leg of my journey I'll be called up so that my visa can be checked as being valid for entry into China. I never travel with hold baggage, so the airline won't have seen me that day or otherwise interacted with me physically.