Might try calling Uniden Support to see if the part is available.
If you go to their web site for the BCD346XT and scoll down through the list of accessories, they list a front case for the BCD396T ($2.64). Obviiously, that is not what you want, but it may just be the web master was lazy and did not customize the accessories for each product.
You can also go to the Sticky at the top of the list of Uniden topics and click on the Archived Sticky thread. Scroll through that for a link that will take you to a wiki screen were you can request part numbers.
When the BCD396T first came out, some had defective silk screening of the labels. As I recall, there were a few posts back then discussing user replacement of the face plate. You might find some information on the replacement process by searching for some of those old threads.