If you breed an egg using the Masuda Method and trade the egg to someone else, would the odds of it being shiny still be raised in the new game it was transferred to?
Nope. Like Silverdragon :D said, the only way the chance of an EGG being shiny gets raised is by trading it to someone who has that TSV. Otherwise, an egg has an equal chance of hatching shiny for everyone. Masuda Method only works for parents.