The platform was developed by a GitHub user under the nickname Pato05. According to Tproger, two versions of the service are available right now: an Android application and a Telegram bot. To use the latter option, just follow the link.
Pato05 also posted information on how other developers can create an iOS and web version of Uploadgram.
Interestingly, the files downloaded via the Android application can be further modified. So, for example, now they can not only be deleted, but also renamed. Also, a distinctive feature of the service is that you do not need to register with it.