So Serebii has the whole list of all the Pokemon and their field abilities right here. However I will actually put in the list of ALL Pokemon here that have a +3,+4, or +5 ability if needed to! (Its Pokemon, Field Ability, and Place):
Cut:
-Roserade +3 Cut Vien Forest (After Quest, Requires River Flow)
-Shiftry +3 Cut Vien Forest
-Starmie +3 Cut Sea of Wailord
-Leafeon +3 Cut Vien Forest
-Umbreon +3 Cut Chroma Ruins
-Fearow +3 Cut Habura Desert
-Vileplume +3 Cut Chroma Highlands (Need +3 Tackle)
-Bellosom +3 Cut Hippowdon Temple
-Honchkrow +3 Cut Oil Fields Hideout
-Scyther +3 Cut Almia Castle, Altru Building
-Sceptile +3 Cut Oil Hideout Fields
-Gabite +3 Cut Hippowdown Temple, Altru Building
-Scizor +4 Cut Altru Building
-Weavile +4 Cut Almia Castle (After beating Boss)
-Absol +4 Cut Asuheru Building, Altru Building
-Flygon +4 Cut Habura Desert (After Final Boss)
-Gallade +5 Cut Altru Building (After beating as Boss)
Recharge:
-Pikachu 3 Recharge Vien Forest, Crysta Lake, Volcano Cave, Chroma Highway, Chroma Highlands, Chroma Ruins
-Raichu 4 Recharge The Ice Lake, Almia Castle,Volcano Cave
-Lanturn 4 Recharge Sea of Wailord
-Magneton 5 Recharge Oil Field Hideout, Habura Desert, Hippowdon Temple, Altru Building, Altru Tower
Crush:
-Crobat +3 Crush Altru Building
-Hariyama +3 Crush Volcano Cave
-Vespiquen +3 Crush Chroma Highway (After quest)
-Glaceon +3 Crush The Ice Lake
-Machamp +3 Crush Oil Fields Hideout
-Walrein +3 Crush Almia Castle
-Abomasnow +3 Crush The Ice Lake (Requires +3 Tackle)
-Glalie +3 Crush Almia Castle
-Frosslass +3 Crush Almia Castle (After Beating as Boss)
-Huntail +3 Crush Sea of Wailord
-Bronzong +3 Crush Hippowdon Temple
-Claydol +3 Crush Hippowdon Temple
-Porygon-Z +3 Crush Oil Fields Hideout (After Final Boss)
-Golem +4 Crush Hippowdon Temple, Altru Building
-Probopass +4 Crush Chroma Ruins (Needs Psy Power +3)
-Sharpedo +4 Crush Puel Sea, Sea of Wailord
-Tyranitar +4 Crush Hippowdon Temple
-Kingdra +4 Crush Sea Of Wailord
-Salamence +4 Crush Vien Forest, The Crysta Lake
-Garchomp +5 Crush** Hippowdon Temple (After beating as Boss)
Soak:
-Pelipper +3 Soak Volcano Cave, Habura Village
-Vaporeon +3 Soak Almia Castle, Altru Building
-Seadra +3 Soak Sea of Wailord
-Omastar +3 Soak Sea of Wailord (After Quest)
Tackle
-Rhydon +3 Tackle Volcano Cave, Habura Desert, Altru Tower
-Ariados +3 Tackle Hippowdon Temple, Altru Building
-Bastiodon +3 Tackle Chroma Ruins, Chroma Highlands
-Piloswine +3 Tackle The Crystal Lake, Hila Valley
-Torterra +4 Tackle Vien Forest (Requires +4 Tackle)
-Aggron +4 Tackle Volcano Cave
-Rampardos +5 Tackle Peril Cliff (After Beating as Boss)
Psy Power:
-Gengar +3 Psy Power Hippowdon Temple, Altru Building, Altru Tower
-Gardevoir +3 Psy Power Altru Building
-Dusknoir +3 Psy Power Hippowdon Temple (After beating as Boss)
-Mismagius +3 Psy Power Almia Castle
Electrify:
-Luxray +3 Electrify Oil Fields Hideout
-Magenzone +3 Electrify Cargo Ship (After beating as Boss)
-Electivire +3 Electrify Oil Field Hideout (After beating as Boss)
-Electrode +3 Electrify Altru Building
-Jolteon +3 Electrify Habura Desert
-Ampharos +3 Electrify Altru Building, Altru Tower
Burn:
-Flareon +3 Burn Volcano Cave
-Camerupt +3 Burn The Crystal Lake
-Infernape +3 Burn Volcano Cave (After beating as Boss)
-Rapidash +3 Burn Chroma Highlands
-Blaziken +3 Burn Asuheru Building
-Arcanine +4 Burn Altru Building
-Charizard +4 Burn Volcano Cave (After beating Heatran)
-Ninetales +4 Burn Almia Castle
-Magmortar **+5 Burn+ Volcano Cave (After beating as Boss)
Hope this helps!