Between RBY and LGPE, all in-game trade Pokemon are completely pre-determined; every value is the same. The only game between these where in-game trade Pokemon can be shiny is in Pokemon XD. Unless the trade is coded to be shiny, the in-game trade Pokemon will not be shiny.
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This is different from gift Pokemon, where some Pokemon can be shiny and some Pokemon can't. This depends on the game and the individual Pokemon.
Hope I could help, please ask if you have more questions! There is a lot of depth to topics like these.