It is time for some maths. Ohh yeah.

So you have a shiny male Typhlosion. According to Bulbapedia shinyness is based on IVs

HP: 0 or 8

ATTACK: 2, 3, 6, 7, 10, 11, 14 or 15

DEFENSE: 10

SPECIAL : 10

SPEED: 10

Now, we come to breeding. The baby gets its IVs from the parent of the opposite gender, so you need to get a female Vulpix.

The Defense IV is passed, while the Special IV has a 50% chance of remaining the same. Attack and Speed are determined at random, at an approximate 1/15 chance. HP has to be 0 or 8

So 1/2 X 1/15 **1/16** X 1/15 **1/16** X 1/7.5 **1/8** = 1/3375. **1/4096** **1/512.**

It's 1/512, that's the final answer, the final one. Whew.

**EDIT: I done goofed up, cheers Unknown Letter Q. I also have messed up on the HP DV. Pardon the constant editing.**

Hope I helped.