I have used affiliate links directly on Twitter on three occasions (from memory). In each instance they were Amazon Associate links and they were a part of a conversation that I was having with other Twitter users (from memory they were at times when followers asked me for recommendations on products). The links that I left were relevant, the conversations were started by others and they fit naturally into the conversation. From memory I declared that they were affiliate links on at least two of those occasions. The opposite of this ‘conversational’ tweeting is the ‘cold call’ tweet which comes out of the blue.
The online lead generation is a multi-billion dollar industry. Done right it can be far more profitable than many imagine. Everyone that I know that is in the business and knows what they are doing, for the most part, does 6-7 figures. While that's a huge range, much comes to one's ability to scale and effectively build / manage the infrastructure needed to scale.