You can use an arduino and follow this tutorial?
https://learn.adafruit.com/adafruit-ein ... duino-codeThe feather will also work with this display:
https://www.adafruit.com/product/3857Here is one working with bluetooth:
https://www.adafruit.com/product/2829There are also more feathers that support WiFi, Sim-card, bluetooth (if you want that)
You can communicate over bluetooth and get the Time that way.
As for the program, I'm not sure about this Android thing.
Also, you would need to program all this yourself. I don't think anyone has built anything like this before.
You can buy buttons here on Adafruit, or find someone on eBay
I'm not totally sure what you are aiming for, but at least I want you to get some thoughts around this maybe.