Only one. It connects to the TV with an hdmi cable.

The Flex box seems pretty limited. If I cancelled cable TV, I think I would just equip my TVs with Roku devices.

It "sounds" to me like one needs to have one device (Roku, Fire stick, et al) per television set.

Which device, if any, allows use for programming more than one television set/receiver?

I think you need a streaming device for every TV or you have a smart TV. In my opinion, the Roku system is the best. Even if you have a smart TV, I would still add a Roku streaming stick because most smart TVs are not as functional as the Roku.

The Flex box will also run some apps like Netflix but I seem to recall it didn't have one of the apps that would have directly competed with Xfinity Cable. So yes, limited. We tried it for a while but ended up staying with our firestick.

But how are you getting internet?
 

I am familiar with the streaming services but all need an internet connection. I have that through Xfinity for $49 a month with no data limit.. What other option would I have?

Have Xfinity internet so just gotta pick something to go with it for TV. Have a smart TV but their shows have too many commercials interrupting. Was going to make a white list for modem but might just try one of the other options mentioned here. Mainly watch TV for NFL plus youtube & have been doing that for about 10 years and just using those under the table streaming sites for live games or movies. Old shows mentioned here I love em so would have to check what has what. I'd watch from the 60s-70s like Star Trek, Hawaii 5-0, Welcome Back Kotter, Charlies Angels, Fantasy Island and even 90s Quantum Leap. Would do a few Outer Limits, Night Gallery etc. too, lot of retro stuff. Sometimes paying full attention, other times for background noise while on computer.