I replied yesterday on your other thread in general discussion; not sure if you would've seen it after the other forumgoer pointed you the direction of the Shipyards here, so just replying here as well!
I captain a D'kyr as my main ship. It's in the same category as the Deep Space Science Vessel (of which I also run), except with a Lt. Com. engineering station and Lt.+Ensign science stations instead of a Lt. Com. science station and Lt.+Ensign engineering stations. Not really a big deal either way unless you're specifically looking to make way for some Lt. Com. skills in engineering, like Eject Warp Plasma. (I personally had to give up Transfer Shield Strength III and got Aux to SIF II, which was a fine deal to me.)
One thing the D'kyr has over the standard DSSV is, of course, the Tal'kyr support craft. It follows and heals whoever you have on target, so 99% of the time, you can expect it to just be tailing yourself for a free Extend Shields I and a pseudo-Hazard Emitters every so often. Launching the support craft can also be useful (or annoying depending on the situation) as it brings your ship to a nearly-instant full-stop. Docking the craft does not impede movement. The support craft itself fires little potshots out of a plasma turret, but while this sounds useful on paper for killing off charged plasma torpedoes or whatnot, I've found in my experience that it gets the little guy in trouble when it goes off to attack targets on which you have no aggro, and then gets blown up. Aggro everything well first, then launch it, and don't let it get into range of any Borg gateways.
You can also requisition the Tal'kyr as a tangible shuttle-class ship and fit it up to your own liking to launch from inside your ship anytime, for the Vault mission or what have you. Apparently, it has the pseudo-Hazard Emitters built into its abilities innate.
The D'kyr currently has several glaring graphics issues. Nothing game-breaking; purely visual, I assure you.
When you dock the support craft, the ring will snap itself jarringly back and forth a few times before getting into the right position (or sometimes not even the right position, staying in horizontal mode until you change maps).
Any special shield graphics enabled on the ship will only display on the main ship, and the vertical ring will remain unaffected.
Then there's the white glow when going to warp or transwarp: currently, the entire aft-port hull of the outer ring will light up, and it just looks ridiculous.
Any engines which add special impulse trail graphics will show one of the trails coming out of the far left side of the outer ring's hull (?!?!?) while the other trail is in the right place, in the back.
And, when you transwarp, you will see the warping graphics first, then once your ship is already gone, the screen will zoom in and you will hear the sound effects. Very bizarre.
Otherwise, I think it's a very classy and wonderful ship. If the Lt. Com. engineering station is something of interest to you, a Nebula also has that functionality to consider, with the added perk that it's a universal station altogether (but of course no signature support craft).