Cyclizar, Shiny Wigglytuff Line from “Shiny Treasure ex”

[ShinyNoivern]

This is only generally true.

Historically, one of the first multi-type attack cost Dragon types was a promo Dragonite with an attack that cost {L}{W}{F}, and I guess you could fudge and say Dragonite's orange body is represented by the brown of {F}, but you'd struggle to find any yellow to match Flygon's traditional {G}{L} attack costs. In Gen 4, Rayquaza C (and Lv.X) has a {W}{P}{F} attack cost that had nothing to do with its body colors and more to do with the typing of other Pokémon C (Milotic C, Spiritomb C, Lucario C).

Presently, it's kind of a mix – you'd be correct that most Dragon attack costs seem to match the colors of their designs, but you'd struggle to find any pink in Zygarde to match the {D}{Y}{C}{C} cost of BUS Zygarde's Core Enforcer, or any green in Giratina to match the {G} present in some of the attack costs of its Gen 8 cards. And sometimes the attack costs owe more to dual typings than colors, as exhibited with many recent Latias cards with {R}{P} attack costs (a mix of both its color and its second type), Altaria with {Y} in its attack costs, etc. Alolan Exeggutor is an example of a Dragon type that circumvents the paradigm altogether and just has {G} and/or {C} attack costs (and some free attacks), rather than implementing any of the quirky attack costs Dragons are known to have.

I think some dragon Pokemon get the energy from the spirit or lore of the pokemon. For example, Dragonite live near the sea and have rescued fishermen, so it gets water energy pretty often.

 

[Frost]

Dragonite: Water, Lightning (from Dragon Vault until SM base, it used Grass, Lightning)

Kingdra: Water, Lightning (a couple Dragon-type Kingdra only need Water)

Flygon: Grass, Fighting (when Dragon Pokemon were Colorless cards, Flygon used Grass, Lightning)
Altaria: Water, Metal (Altaria GX uses Water, Fairy; when Dragon Pokemon were Colorless cards, Altaria used Water, Lightning in Gen 3)
(Mega) Salamence: Water, Fire
Latias: Fire, Psychic (when Dragon Pokemon were Colorless cards, Latias used Water, Fire and rarely Psychic)
(Mega) Latios: Water, Psychic (when Dragon Pokemon were Colorless cards, Latios primarily used Grass, Lightning and rarely Psychic)
Rayquaza: Fire, Lightning (Rayquaza C uses WPF; Rayquaza GX uses Grass, Lightning)

(Mega) Garchomp: Water, Fighting
(Origin) Dialga: Psychic, Metal (often just Metal)
Palkia: Water, Grass (often just Water)
(Origin) Giratina: Grass, Psychic

Haxorus: Fighting, Metal (Unified Minds's Axew, Fraxure and Haxorus use Fire, Metal for some reason)
Druddigon: Water, Fire
Hydreigon: Darkness, Psychic
Reshiram and Zekrom: Fire, Lightning (they almost always are printed as R/L instead of Dragon - one Dragon Zekrom needed only Lightning)
Kyurem: Water, Metal or Psychic (its debut Dragon card in Gen 5 was W/P, Evolving Skies Kyurem was W/M - some Dragon Kyurem only need Water)
White Kyurem: Water, Fire
Black Kyurem: Water, Lightning

Mega Charizard X: Fire, Darkness
Dragalge: Water, Psychic
Tyrantrum: Fighting, Metal
Goodra: Water, Fairy (now Water, Psychic)
Noivern: Psychic, Darkness
Zygarde: Grass, Fighting (one Complete Zygarde card in gen 7 used Darkness, Fairy; one 50% Zygarde card in Dragon Majesty used Fighting only)

Alolan Exeggutor: has only ever needed Grass and Colorless on its Dragon cards
Turtonator: Fire, Fighting (Turtonator only has two Dragon cards and the first used only Fire energy)
Drampa: tends to need all Colorless energy; Evolving Skies Drampa is the only outlier with other energy requirements (Water/Fighting)
Kommo-o: Lightning, Fighting
Guzzlord: its only Dragon print was its tag team with Naganadel, which used Darkness, Psychic
Ultra Necrozma: Psychic, Metal
Naganadel: Lightning, Psychic on its only solo Dragon card

Hisuian Goodra: Water, Metal
Flapple/Appletun (and presumably Dipplin): Grass, Fire
Dracovish: Water, Grass
Duraludon: Fighting, Metal
Eternatus: Fire, Darkness
Regidrago: Grass, Fire

Cyclizar: Grass, Darkness
Tatsugiri: only Water so far

Mega Ampharos, Mega Sceptile, Origin Palkia, Necrozma, Dawn Wings/Dusk Mane Necrozma, Dracozolt, Dragapult, Eternamax Eternatus, Baxcalibur, Koraidon, Miraidon, Roaring Moon, Walking Wake, Dipplin, Archaludon: never printed as a Dragon card yet

It's not an exact science, especially when there are dragons who don't match the colors of the TCG types perfectly (and/or they're trying to avoid overlapping the type combinations as much as they can), but there's a correlation. It's kind of like how delta Pokemon tended to be, but weren't always, the same type of their main body color.

 

[Frost]

You know, I'll actually retract that comment about the Delta Species. I was mostly thinking of the later era ones when they'd all stopped being part Metal, but even re-examining those, it doesn't work. It's just a thing that latched into my brain years ago because my two favorite Pokemon fit the "pattern" (Dewgong is white and Dewgong delta is Colorless, Jynx is red and Jynx delta is Fire).