There is no set amount of chains that will guarantee that you will encounter a Pokemon with six perfect IVs; your chance of finding a Ditto with six perfect IVs is therefore left down to probability. Unfortunately, that probability is not in your favour at all. With the chaining method, you're going to run into a lot of 4 IV Ditto like the one you have, a few 5 IV Ditto and almost none with 6 IV. If you're after a 6 IV Ditto only, chaining is not worth your time.
The highest amount of perfect IVs you can guarantee with the chaining method is four, which is achieved with the 30th chain. After that, any further perfect IVs (ie. a fifth or sixth) are based on pure luck. Your chances of finding these is fairly simple probability: for 6 IVs it's simply (1/32)^2 which is 1/1024, abysmally low for something you can only attempt each time a 30th Pokemon is chained.
If you'll settle for a 5 IV Ditto -- which is usable but will take a bit longer whilst breeding -- your chances of finding one are 63/1024, or about a sixteenth. (That's the chance of one IV being perfect added with the chance of the first one not being perfect and the second being perfect, or 1/32 + 31/32 * 1/32.)
The sad reality is that there is no easy way to get a 6 IV Ditto. If you'll accept a 5 or 6 IV Ditto whilst chaining, you can have 6.25% chance of getting one each time you chain to 30 Ditto -- otherwise, you'll have to look elsewhere. Pokemon sub-Reddits, especially /r/BreedingDittos, /r/pokemongiveaway and /r/PokemonTrades, are the best places to look in my opinion as they have the largest group of people all looking specifically to make trade deals.
Basically, it's possible but highly improbable that you will find a 6 IV Ditto using the chaining method.