You can copy a join recipe in DSS 4.1 and later, but you will need to also copy the dependent datasets you can use the following steps:
From your flow select the join recipe and output dataset
This will show a Copy option under Other Actions in the in the Actions Panel
Then you can select the project you can select Copy To and select the destination project
Please note that this will share the dependent datasets to the new project which you can later choose to "Stop sharing to this project" from other actions if you need to to use different datasets for that particular join you've copied.