Without shiny charm.

SHINY CHANCE A chain length of 70 to 255 gives you a 1/1024 chance of encountering a shiny (normally 1/4096). If you have obtained the Shiny Charm, the chance becomes 1/683. Source

After a chain of 70 the game rolls the shiny chance an extra three times, meaning the normal chance of 1/4096 gets increased to 4/4096, effectively giving a chance of 1/1024. With a shiny charm, this chance is originally 3/4096 (two extra rolls for shiny spawn), and so gets boosted to 6/4096 after a chain of 70, effectively giving about a 1/683 chance of a shiny until the chain counter rolls over to 0. Source

After 70 chains, the Shiny chance is 1/1024 (0.097%) or 1/683 (0.146%) with the Shiny Charm.