Stamps are a small image or gif, the typical sizing being 99x56 pixels big. they have a border around them similar to postcard/mail stamps, which is where their name comes from. They've been around almost as long as gifs in general, you'd see a lot of them around on personal sites inn the late 90s and early 2000s. They started out simple to make and still are, you can make them with almost any digital art platform. Here's a little tutorial on how to make them so that you can make your own.
most if not all drawing software, from MS Paint to Clip Studio Paint, you can make a blank drawing known as a canvas. you'll want the width to be 99px and the height to be 56px. Make sure the canvas is transparent, this is important when it comes to making the border.
you'll want to make the design, you can make it whatever you want. either import an image and size it down to fit or draw* out a design yourself. You'll want to leave the outer 3 pixels transparent here.
*Note: if you want it to look like actual pixel art and not just blurry, check your software tools to make sure anti-aliasing is turned off. this gives the pixels a hard edge.
Stamp borders usually are about 3 pixels around the blinkie. the detailing is usually triangle shapes around the border, with "shading" on the sides and bottom. Sounds complicated, I know, but here's all it is ↓
Now, you could be done here, or you could animate it.
Stamps don't really have a set number of frames like blinkies do. Some drawing programs already come with an animation feature for free, but if your platform either paywalled that option or simply doesn't have it, you can use a gif maker site and import each frame manually.