Bulgarian ring dips vs planche

I'm currently working on FL , Planche and side levers but on my triceps/chest training day i do some bulgarian ring dips and i'm feeling like something(maybe this ring dips) is using a lot of my shoulders and i  cannot recover my muscles enough to achieve those skills;

I'm able to do a lot of them, but can it harm my goals? Should i finish everything related to the foundation series before moving to anything related to the rings one?

yes

The original post is ambiguous.  If you are doing foundation, then you are working through FL, SL, and SPL progressions, and it can be reasonably inferred that the trainee is following the programming associated with Foundation.  Conversely, the trainee has a "tricep/chest" day, which implies a traditional body building program.  The very question suggests that Foundation is not being followed, as Bulgarian dips feature in the Foundation progressions.  If FL, SL, and SPL are the goal, follow the progressions in Foundation, and the inclusion of Bulgarian dips in the workout will come together.   Once mastered, they can be done in warm-up or after Foundation sets are completed, as recovery allows, just because they are so very good.  

All Foundation course questions in the relevant forum please if you are following this course then your question is completely covered.

Otherwise, Bulgarian dips are excellent but fall under the category of basic strength, not rings strength. They don't require a long, solid support position, for example. They should be worked and mastered as detailed in the course as a step on the road towards rings strength. Good aa they are, it's not like they're cross pulls

And yes, Bulgarian dips can be very taxing on the shoulders, particularly if your mobility is lacking. Done right, they are not a beginner movement. Chances are, if you are just throwing them in, they are responsible for tiring you out

How much stability in the rings support would one need for Bulgarian dips, or rephrased; what would be a good standard for rings support holds to adequately support the Bulgarian ring dips?

at least 10-15 seconds, considering that every repetition should end into solid and temporary support hold. 

if you are too new on this movement you can consider to reduce the stress on the elbows by holding the upper arm in contact with upper body.