Thanks' for the replies.
I can copy a flow which includes the env variables set on its tab, but I cannot copy these env variables to another flow - only a new flow.
I tried the suggestion of creating a group with the env variables, but these are scoped to the group, so also not useful in this case.
I think I will create a single env variable that contains a json object containing all the constants I need to use. At least this can be manually copied in a single step.