There's a difference between painting and uploading.
To paint a skin image, you need some kind of art software, like Photoshop or FireAlpaca. It's best to do this on a computer... but there are some free apps for phones as well, like Medibang Paint Pro (I tried it once, it's safe). When the drawing is finished, you save the image as a .png file.
(you don't actually need to draw digitally - you could draw a gryphon or something on paper, take a photo or scan it, and then erase the white background so it's transparent. This will still require some art software. If that's too difficult, you could send the image to me or another arty person and we could "cut out" the background for you.)
Then you go to the BK custom skin page, that's where you choose the image from your computer/phone's files, and enter the details for the skin. Same as uploading art to Imgur or DeviantArt etc, if you're familiar with those.
Does that help a bit? :)
... oh, or is it a problem downloading and editing the official bases from that page? You need art software on your computer/phone, to open and paint over those images. The BK website itself does not have painting functions. It just links you to the images so you can download them to your device.
If it's tricky to edit the bases digitally, I guess you could try copying the beast outlines onto paper, and colouring them that way.