Synchronoise is learned by 16 species by level and 5 by egg

Effect, in PokéAPI's words

“Hits any Pokémon that shares a type with the user.”

Who learns it

21 species in all, 6 games

Ultra Sun and Ultra Moon: 21 species

Species	Method	Level
Chimecho	Level up	1, 52
Beheeyem	Level up	1, 63
Munna	Level up	25
Sigilyph	Level up	31
Drowzee	Level up	37
Hypno	Level up	37
Hoothoot	Level up	43
Whismur	Level up	43
Bruxish	Level up	44
Chatot	Level up	49
Loudred	Level up	50
Kecleon	Level up	50
Noctowl	Level up	51
Exploud	Level up	53
Elgyem	Level up	53
Magearna	Level up	73
Psyduck	Egg
Eevee	Egg
Natu	Egg
Ralts	Egg
Woobat	Egg

Sun and Moon: 21 species

Species	Method	Level
Chimecho	Level up	1, 52
Beheeyem	Level up	1, 63
Munna	Level up	25
Sigilyph	Level up	31
Drowzee	Level up	37
Hypno	Level up	37
Hoothoot	Level up	43
Whismur	Level up	43
Bruxish	Level up	44
Chatot	Level up	49
Loudred	Level up	50
Kecleon	Level up	50
Noctowl	Level up	51
Exploud	Level up	53
Elgyem	Level up	53
Magearna	Level up	73
Psyduck	Egg
Eevee	Egg
Natu	Egg
Ralts	Egg
Woobat	Egg

Omega Ruby and Alpha Sapphire: 19 species

Species	Method	Level
Chimecho	Level up	1, 52
Beheeyem	Level up	1, 63
Munna	Level up	25
Sigilyph	Level up	31
Drowzee	Level up	37
Hypno	Level up	37
Hoothoot	Level up	41
Whismur	Level up	43
Noctowl	Level up	47
Chatot	Level up	49
Loudred	Level up	50
Kecleon	Level up	50
Exploud	Level up	53
Elgyem	Level up	53
Psyduck	Egg
Eevee	Egg
Natu	Egg
Ralts	Egg
Woobat	Egg

X and Y: 19 species

Species	Method	Level
Kecleon	Level up	1, 58
Chimecho	Level up	1, 54
Beheeyem	Level up	1, 63
Munna	Level up	25
Sigilyph	Level up	31
Drowzee	Level up	37
Hypno	Level up	37
Hoothoot	Level up	41
Whismur	Level up	41
Noctowl	Level up	47
Chatot	Level up	49
Loudred	Level up	51
Elgyem	Level up	53
Exploud	Level up	55
Psyduck	Egg
Eevee	Egg
Natu	Egg
Ralts	Egg
Woobat	Egg

Black 2 and White 2: 19 species

Species	Method	Level
Munna	Level up	25
Sigilyph	Level up	31
Drowzee	Level up	37
Hypno	Level up	37
Hoothoot	Level up	41
Whismur	Level up	41
Noctowl	Level up	47
Chatot	Level up	49
Loudred	Level up	51
Elgyem	Level up	53
Chimecho	Level up	54
Exploud	Level up	55
Kecleon	Level up	58
Beheeyem	Level up	63
Psyduck	Egg
Eevee	Egg
Natu	Egg
Ralts	Egg
Woobat	Egg

Black and White: 19 species

Species	Method	Level
Munna	Level up	25
Sigilyph	Level up	31
Drowzee	Level up	37
Hypno	Level up	37
Hoothoot	Level up	41
Whismur	Level up	41
Noctowl	Level up	47
Chatot	Level up	49
Loudred	Level up	51
Elgyem	Level up	53
Chimecho	Level up	54
Exploud	Level up	55
Kecleon	Level up	58
Beheeyem	Level up	63
Psyduck	Egg
Eevee	Egg
Natu	Egg
Ralts	Egg
Woobat	Egg

Changed over time

2 changes since Generation V

1. Through Gen VPower 70120 from X and Y, Generation VI
2. Through Gen VPP 1510 from X and Y, Generation VI