I have many apps from my 920, that they don't carry in the store anymore (Chase, Vevo, etc).
That sucks.
How can I sideload these apps onto something like a Lumia 640 via the SD card?
You can't. As a developer, you can side load apps that you have written for testing, but even developers aren't able to side load other's apps without decompiling them and recompiling, which is against the law.
On a slightly related note, I was able to download Crackdown 2: Project Sunburst onto my 920 running W10M.
It was in my list of purchased apps in the app store so I thought I'd give it a go. It downloaded without a problem. However, I was met with a "server down" message when I loaded it up.
Anyway, my point being maybe you can get hold of these apps in W10M if you're willing to give it a try.
Yeah, Chase was nasty about it and actively blocked the app. For a short time, they even blocked IE in Windows Phone from accessing the web site. I think they only meant to block the app, but were over zealous in the block.