There is no way to 'keep the bit depth of 24bits' when converting DSD to flac (or any other codec), since DSD isn't 16, 24, 32 or whatever bit depth. Simply put, it's a whole different beast, and actually a 1 bit streaming algorithm.
So when you convert it to another format, you are actually transcoding, so you are changing the sound quality.
I believe MusicBee will transcode dsd to 16 bit bit depth. I am guessing it will probably keep the same sample rate as the original dsd file.
Other tools might have optional settings to transcode to 24 bit, or set required sample rates.
The values of 1556 and 2822 you mention are bit rates, not bit depths. They only say something about the average rate the file streams through your decoder (player).
It doesn't say anything about bit depth, sample rate, audio quality etc.
Well, of course a very high value might make it probable you are dealing with a 24/88 file, but you can not calculate anything from it.