If i added a Reishi Mushroom kit into a plant pot with wooden chips would the mycelium take over?

would the mycelium eat the wood chips? also how much moisture does the reishi kit need? my reishi kit seems to be drying and dying.

As far the health of the mushroom, you can't go wrong with good mulched soil in the ground (ie, natural, unadulterated environment) - is there any reason they need to be in the pots specifically?

yes the mycelium would eat the wood chips, Reishi generally are found on logs or stumps in the wild, that is why most people inoculate logs to grow them.

You can also grow them in wood chip enriched soil as Dustin mentioned.
If you are going to use pots to contain the mycelium, be ready to take a portion of it later on to start new pots of wood chips. (hard woods are best for Reishi growing.