Hi vdcarroll, and a big
to ATP. So glad you found your way here.
Tim made some great comments. It would be very helpful to see photos of your seedlings and what appears to be blooms. It would also be helpful to know what growing zone you are in.
Most succulents don't do well indoors for extended periods of time, and by your description it sounds like they are etiolated (stretching up to find light).
No, the bloom is not what you plant to have succulents. Eventually the blooms will mature and form seed, if they get pollinated. The seed is what you would plant for more succulents.
We all look forward to seeing your photos.
A sempervivum bloom.