You shouldn't lose any emblems or progress on your Playstation account by linking it with your XBOX account or visa-versa . Just make sure you're logged into your account that has the emblems you've redeemed with codes (if any) here on Bungie.net then going to settings>Accounts&Linking> and link from that page, do not attempt to link the account while signed out because it can cause you to create a new Bungie.net profile. view this article for more information: https://www.bungie.net/en/Help/Article/12130

You can link up to two console accounts to your bnet profile, however they cannot both be in the same console family, so you can link one PSN ID, and one Xbox gamer tag to a single bnet profile. When you login, you'll select which console family to login under, and use the credentials for that ID or gamer tag. You could easily switch back to the other ID or gamer tag by logging out and logging back in to the different one. Nothing is lost by linking to a second console account. Under certain circumstances, you can orphan an account by un-linking it, but you should have nothing to worry about simply adding a different console account to your bnet profile. https://www.bungie.net/en/help/article/12130

You have to be careful when linking accounts. Personally I've never had to link multiple accounts, but from what I've read it is possible to lose access to certain items if done incorrectly. Wish I could give a better explanation, but figured I'd give you a heads up regardless.