There may (probably will) come a day when Flash for Android will stop working entirely. If Key Lime Pie (reportedly the code name for the next Android version due out later this year) turns out to be incompatible with the sideloaded APK files, put a fork in it, we're done.
There WILL come a day when it stops working for a lot of sites. The current version of Flash is 11. As sites start migrating to 12 (or 13 or 14) over time, if web developers start using features specific to those versions and requiring those versions at a minimum, we won't be able to see those sites.
But for the foreseeable future, the majority of Flash-based sites should work just fine on the Nexus 7 and any other Jelly Bean or earlier device, for the vast majority of web sites.
The only difference tomorrow is if someone comes to you with a Gingerbread or Ice Cream Sandwich Android and asks how to put Flash on it, you'll have to enable sideloading and install two APKs that you have to download, rather than just telling them to find Flash in the Play Store. For Jelly Bean, Adobe has already pulled Flash (it never put a Jelly Bean version out there in the first place) so we already have to sideload it. That's why this announcement means absolutely nothing to Nexus 7 users. This change just makes ALL devices require sideloading, just like the Nexus has always required.
Plus, I think security updates are going to be harder to find and apply. Right now, when Adobe makes a security update available, it shows up in the App Store as an upgrade. In the future, you'll have to go looking for it, meaning people might continue running insecure/unpatched versions of Flash longer. This is going to be a problem long-term, as it is for any sideloaded apps that don't come from some sort of curated app store with update notification.