Short answer: You can't.
Long answer: You cannot or may not record streaming content, for both technical and legal reasons.
For some who are new to streaming, this may not make much sense. After all, if you subscribe to Sling TV (for example; any streaming service could be the example), you get cloud DVR functionality. So why can't you use a Tablo or other similar device to record streaming content.
Well, let's think for a second. When you record content from Sling TV using their cloud DVR, where is that content stored? That's right, in the cloud. And what is the cloud? That's right, it's somebody else's computer. And it's computers owned or controlled by Sling TV (in our example).
That means that the folks who got the original stream from the network and formatted that content to work with streaming are the ones who made the recording. They got to it before it ever went out the Internet from their servers to your location. It was all done "in house."
What they did with the streaming content was essentially turn it into what Hulu has: content that was sent out live earlier but nor in an on-demand format rather than a live streaming format (yes, they're different).
In order for, say, Tablo to record the streaming content, you'd need to feed it from your Roku (or other streaming device) to your Tablo. And the content from an on demand stream is a different format than the content Tablo is designed to get, from an antenna.
Sure, to you, they seem the same. But they are not the same, and being able to record one format (the over the air content) is not at all the same as being able to record live streaming content.
Besides the technical issues, there are the legal issues. I won't go deep into this, but the summary of it is that Tablo (or other local DVR) can't legally record it. Over the air is one thing. Streaming is a very different other thing.
If I want to keep content for a long time (what passes for forever), I'll simply buy the content. I can still watch it live if I want, or I'll watch it after it comes available via the purchase.
You may have noticed that I didn't say flat out that it is totally impossible. The Short Version was a summary only. The Long Version never said it was 100% impossible. Rather, I mentioned the obstacles with it, including the legal issues.
I'm not one to suggest, nor offer assistance to, some who breaks the law. I'm saying don't do it. I won't help you get around the legal stuff with technical stuff. Others might, but I won't.
I want to enjoy my Streaming Life knowing that I'm doing the right thing, and not depriving anyone, even a large fat company, of what is legally theirs.