Alongside the latest Team Rocket Balloons appearing in Pokémon Go, a new branding option may appear at any time. Some players have encountered a rare Meowth ball, and clicking it gives them a chance to challenge Jessie and James, the dynamic duo from the Pokémon anime and TV show. Rumor has it that these two will show up, but it's now been confirmed that you can meet and fight them in the game.
Unfortunately, for the Meowth balloon to appear on you, it's a random chance. There is no direct way to get there. It appears much like other Team Rocket balloons, where it appears floating above your character, and you can interact with it. When you see a Meowth balloon and touch it, instead of Team Rocket Grunt, Leader, or Giovanni talking to you, it's Jessie and James.
These two will have their own set of Shadow Pokémon to rescue, just like the other members of Team Rocket. You have the chance to rescue these Pokémon from the shadows, their potential choices being the shiny variants. You can also purchase free outfits for your avatar in Pokémon Go from notable outfits of Jessie and James from the original TV show. These are available for free in the store.