Overview / History
Dragunity is a weird archetype in the broad scope of Yu-Gi-Oh's history. They revolve around equipping Dragon-type Tuner monsters to their other monsters in order make Synchro plays. While their notorious Field Spell Loading... has plagued the TCG with its amazing ability to dump Dragons from your Deck to the GY (also it searches Dragunity cards or whatever but don't worry about that). Outside of that one busted card, however, the archetype itself, despite having over 30 cards to its name (most of which are in Duel Links btw), hasn't made much of a splash outside being an engine for other decks.
That brings us to Duel Links, where the archetype debuted in Blackstorm Rising, which was basically a set-up box for both Blackwings and Dragunity. In this box we got the shamblings of a gimmicky OTK deck with Loading... , Loading... , Loading... , Loading... , Loading... , Loading... , and pseudo-support in Loading... . The deck had problems of only wanting to go second and only with some way to clear the opposing backrow to avoid ubiquitous cards like Loading... and Loading... (a running theme throughout the lifespan of this deck).
The deck stayed that way with basically no support (yes Loading... your presence is acknowledged now go back to your corner) until the release of Dragunity Overdrive, giving the deck Loading... and the means to make it with Loading... and Loading... . This structure deck was ok for Dragunity, as now you had a decent turn one play in Ascalon and a HUGE consistency booster in Senatus. However, the deck still had the same problems of not being able to play through backrow, with the new problem of not being able to OTK reliably with Ascalon's awkward 3300 ATK.
Then comes Judgement Force, offering only a single card to support the deck in Loading... , but what an amazing card it was. Couse offers the deck so much, boosting the OTK-ability of the deck drastically. The deck still faces the problem of being unable to play through backrow, but I feel like Couse is what the deck needed to bring this deck to the competency of more traditional OTK decks.
Core Cards
Main deck
Dragunity Senatus (3x)
Senatus is your starter, as its effect is a one-card Loading... (or any other Dragunity Synchro for that matter). Senatus, when combined with a Loading... (and by extension Loading... ) discard is what allows you to OTK. Note that he is super vulnerable to disruption, as it is an Ignition Effect that discards as cost, but its the strongest opener you have access to. Senatus also has a destruction prevention effect, which is cute when paired with cards like Loading... , but it's ultimately not what the card is used for.
Dragunity Couse (3x)
Couse is one of the strongest cards in the deck, which is weird considering it basically does nothing on its own. Couse is functionally similar to Loading... , as it shares the effect to special summon itself from the Spell/Trap zone. However, it boasts 2 distinct and important differences: the ability to be trated as a Level 4 for the Synchro Summon of a Dragunity Monster and a higher ATK Stat. These distinctions let you go into Loading... through Loading... , which when combined with Couse's 1000 ATK is what allows you to OTK much more reliably. He also adds redundancy for things like the Loading... engine, acting as another target that actually wants to be in the GY.
Dragunity Dux (1-2x)
Dux is primarily used for follow-up plays, as it requires a Dragunity in your GY. It also serves as another Level 4 Equip target for Loading... letting you fetch Loading... and go into Loading... . Dux is the main card you want to see in the later turns, once you're already set up with Couse in the Graveyard, but has more value in the Loading... build, which lets you set up your GY on the first turn.
Extra Deck
Dragunity Knight - Ascalon (2-3x)
Ascalon is your primary boss monster, similar to Loading... allowing you to banish your opponent's monsters as long as you have fuel in your GY. It also has a floating effect on destruction, letting you summon Loading... or Loading... for follow up plays, or Loading... for more safety. If you're going first, Ascalon in DEF is your best Turn 1 play for ensuring you get to Turn 3 and OTK.
Dragunity Knight - Barcha (2-3x)
A monster that used to be practically impossible to summon is now your primary stepping stone to Loading... and a key component to your OTK engine. You make Barcha with Loading... / Loading... and Loading... . On Synchro Summon (note Ascalon's floating effect counts as a Synchro Summon) you can equip as many Dragon-type Dragunity monsters as possible. If you equip 2 of either Couse or Loading... , you're able to summon Ascalon with an ATK Position Couse, allowing you to banish your opponent's monsters and push 4300 Damage. It can also potentially protect your Life Points post-Ascalon Destruction with its up to 2900 ATK.
Dragunity Knight - Gae Bulg (0-1x)
This monster is primarily summoned off of Loading... 's effect. It's effectively a 3800 beatstick as long as you have Loading... in GY, which provides you with an added layer of protection if Ascalon is destroyed on your opponent's turn. However, this protection is in lieu of the follow-up plays Loading... (and by extension Loading... ) provide. If you're up against a lot of big beaters, Gae Bulg just might be able to save you from lethal.
Dragunity Knight - Vajrayana (0-1x)
This card has gotten much less useful since the deck has shifted away from Loading... . It can equip Loading... on summon, letting you go into Loading... (however, Loading... performs this role better). In the Loading... build, you would run Vajrayana as a contingency that can be summoned with Loading... + Loading... (If you happen to have drawn / discarded all of your Couse). Its secondary ability to boost its ATK to 3800 (or 5000 with Divine Lance) is situationally useful but more-or-less irrelevant.