In the standard, no - this is not provided.
However it IS technically feasible with a little hack.
Set a break point in the location shown by the screen shot below, then go to the admin transaction and copy the SMEN flavor to a new name. When the process stops at the break point, change the transaction code in field gs_flavid_db-tcode after this line, using the replace feature of the debugger.
Now while this will work, you have to handle this with caution. It only makes sense to copy a flavor from one transaction to another if the two transactions are VERY similar, like in many cases the Display and Change transactions of the same object, for instance. Like Change Sales Order / Display Sales Order. However even then, you may encounter some weird problem or even slight differences of these transactions can cause unexpected effects.
Under no circumstances is this supported by SAP though 
So in case of any problem resulting from doing this, you're on your own.
However in your case, since you copied a standard transaction to a custom one, this will probably not work because the program name of the copied transaction is different, so the resulting control IDs of your custom transaction will then also be different. The flavor has customization for different controls than the ones on the screen, so you'll then end up with the flavor looking like the Basic View. I never tried to do this on such a copied transaction, but that's my expectation.