Our coffee mugs happen to be fleishig, used with chicken soup, etc…is it permissible to pour soy milk made from dairy equipment into a hot fleishig coffee mug?
Yes it is permitted. Although the Ashkenazi minhag is not to eat food cooked in a dairy pot with meat , it is however permitted to place that food into a meaty pot. Especially in this case when it was already cooked in the dairy equipment, and you didn’t cook it with the intention to put it into the meaty pot, it is permitted.
Rema Y:D 95-2,