Dratini is not the easiest Pokèmon to come across out of all the available Pokèmon. Some trainers are still struggling to find one, or find more to evolve their Dratini into Dragonite.
Dragonite is one of the most powerful Pokèmon in the game so it’s no wonder trainers want to get their hands on one or at least enough Dratini to evolve into Dragonite. Dratini usually have about a 5-7% spawn rate in certain areas so it’s not that easy to find them.
One trainer on reddit explains his experience on catching Dratini’s while farming Magikarp. It might lead you to find your own Dratini and start farming them:
With the update a few weeks ago, new Pokemon spawn locations were added along a paved walking trail (marked on Google maps) next to my home. This trail runs alongside a creek, and I noted that there were 2 distinct spawn points consistently showing Magikarps…one spawned at about :15 after the hour, and the other :40 after the hour.
While farming Magikarps, I started to note the occasional Dratini at these same locations…they were showing up once a day. For the past 3 days, I have been able to farm the Dratini…the first day they showed up at 20:15 and 20:40; yesterday they showed up at 16:15 and 16:40. Although the Dratini show up on my nearby list…I have to jog about 1/2 mile to reach them because a cliff that runs alongside the creek behind my house restricts direct access. Today, I decided to get a headstart, theorizing that maybe they were spawning every 20 hours. I walked down there at 12:00…and sure enough the Dratini spawned at 12:15 on one location and 12:40 at the other.
There you have it. Start checking Magikarp spawn points and see if you can catch a Dratini, if so start timing it and see if you can tell how often it spawns there and go there everyday until you have enough Dratini to evolve a Dragonite.