Is publishing my story like this likely to be successful?
I doubt it, I doubt enough Kindle readers would be interested.
If by "published" on Kindle you mean sold on Kindle, I think you have a marketing issue. Sold at what price? Who is going to buy the first installment, knowing it is not a complete story? Thirteen episodes, at 99c, is $12.87, almost twice the price of a published book by a well known author. You are competing with 99c novels, and $2.99 novels by known authors, not to mention the free Kindle offers.
You might get some takers if it was all free, but can they trust you to make the final installment free? Can they trust you to even finish the 13 episodes you promised?
And even then, if I'm willing to try an unknown author, it would be worth it to pay 99c for a whole book I can read in a week, that I know is done, instead of reading 13,000 words on a Saturday morning (less than an hour for most people) and having to remember the book for a week before I read the next installment.
I think the instant gratification demands of the modern world, along with the problematic cost structure and trust issues, will leave you with a very tiny audience.
There is a difference between a book and a television show; TV is a visual experience, with recognizable characters, and typically an easily remembered plot line in progress. A book is a literary experience that all happens in the reader's head and imagination. It isn't as easy to remember as turning on a TV show; the show writers and actors make sure you remember the characters and setting and what happened "previously". Unlike Dickens's time, in the modern world, I think there are too many other things competing for our memory for this approach to gain any traction.