As another commenter already mentioned, this is exactly the idea behind the World Food Programme's app called Share The Meal. It is quite a successful app.

The closest thing to the app you want that I know of is this app from The Life You Can Save, which I was part of developing when I was working at Meepo. We really liked the Share The Meal app and wanted to create something similar for effective charities. 

Payment is not complicated; you just need to integrate a payment provider such as Stripe or Adyen. However, one problem with these payment providers is that they charge per transaction. This hits micro-transactions such as $1 especially hard. For Stripe, for example, the fees for European cards are 1.5% + 0.25€. For many people this might not be an issue but to me it feels wrong that more than 25% of my donation would go to the payment provider. But if the app is just for fuzzies and not your main way of donating, perhaps it could be fine.

As others have pointed out, you won't be able to create a button that you can "spam" to donate because Apple and Google won't allow it. Maybe your internal tally idea would be allowed by Apple and Google, I am not sure.

Thanks for making this post, I really like this app idea and I'm glad others do too.

Thanks for mentioning this, I was going to post this myself.

Sounds like fun! Please add me to the Signal group. :)

Just want to let you know that https://cancelcorona.org/ shows an error message, and it's linked to on the front page of https://givemomentum.com/.