Before I give an answer, there's a couple things I need to mention.
1. The difference between a check and counter:
Pokémon A checks Pokémon B if, when Pokémon A is given a free switch into Pokémon B, Pokémon A can win every time, even under the worst case scenario, without factoring in hax. Pokémon A counters Pokémon B if Pokémon A can manually switch into Pokémon B and still win every time, even under the worst case scenario, without factoring in hax.
Source
The difference is that a check can force out a Pokemon provided it gets a free switch that doesn't punish it, while a counter can freely switch in and can still win every time.
2. The sets Falinks uses in Gen 9 PU:
Knowing the sets Falinks uses will help determine which Pokemon can switch into it. The sets it can use are a No Retreat set and a Choiced set. Here are the sets:
Falinks @ Lum Berry / Life Orb
Ability: Defiant
EVs: 252 Atk / 4 Def / 252 Spe
Tera Type: Ghost / Dark
Jolly / Adamant Nature
- No Retreat
- Close Combat
- Rock Slide / Iron Head
- Tera Blast
Falinks @ Choice Band / Choice Scarf
Ability: Defiant
EVs: 252 Atk / 4 Def / 252 Spe
Tera Type: Ghost / Bug
Jolly Nature
- First Impression
- Close Combat
- Rock Slide
- Tera Blast / Iron Head
Source
With Falinks using these moves the Pokemon that can switch into it are Misdreavus and Gabite when they Tera into a Fairy-type.
Misdreavus
Misdreavus @ Eviolite
Ability: Levitate
Tera Type: Fairy
EVs: 216 HP / 220 Def / 16 SpD / 56 Spe
Timid Nature
IVs: 0 Atk
- Will-O-Wisp
- Hex
- Pain Split
- Power Gem
Misdreavus's physical bulk with an Eviolite and investment can let it switch freely into Close Combat, First Impression, and Rock Slide. Misdreavus can switch into a Choice Scarf Falink's Iron Head, though it can only do that once. Misdreavus can use Will-O-Wisp to burn Falinks so it can proceed to use Hex or Pain Split afterwards, though it has to be careful of Lum Berry Falinks.
252 Atk Falinks Iron Head vs. 216 HP / 220 Def Eviolite Tera Fairy Misdreavus: 110-130 (34.9 - 41.2%) -- guaranteed 3HKO
However, Misdreavus can't really switch into a Choice Band/+1 Iron Head and a +1 Life Orb/Adamant Choice Band Tera Blast Ghost from Falinks.
Overall, Misdreavus can counter Choice Scarf Falinks, and check Choice Band/No Retreat Falinks.
Gabite
Gabite @ Eviolite
Ability: Rough Skin
EVs: 252 HP / 136 Def / 92 SpD / 28 Spe
Tera Type: Fairy
Impish Nature
- Stealth Rock
- Earthquake
- Stone Edge / Dragon Claw
- Dragon Tail
Gabite @ Eviolite
Ability: Rough Skin
EVs: 252 HP / 136 Def / 92 SpD / 28 Spe
Tera Type: Fairy
Impish Nature
- Earthquake
- Dragon Tail
- Rest
- Sleep Talk
Pretty much the same case as Misdreavus of what Gabite can and can't switch into. (can't really switch into a Choice Band/+1 Iron Head and a +1 Life Orb/Adamant Choice Band Tera Blast Ghost from Falinks.) Gabite's Rough Skin is useful for punishing Falinks for using moves like Close Combat, First Impression, and Iron Head. Gabite has Dragon Tail to force out Falinks, which is useful vs the No Retreat Falinks set. Gabite also can heal off the damage taken vs Falinks if it uses the RestTalk set.
Since Earthquake doesn't do a whole lot of damage to Falinks, Gabite is a check to No Retreat Falinks and Choice Locked Falinks.
TL;DR There aren't really counters for Falinks, but rather checks. The closet counter to Falinks would be Tera Fairy Misdreavus vs the Scarf set. Otherwise, Tera Fairy Misdreavus and Gabite can check Falinks. I'd also like to mention that Falinks isn't as common in the current PU metagame, so Falinks shouldn't be too big of a problem.
Hope this helps!
