"Matěj a jeho bratr jsou moji strýci."

Translation: Matěj and his brother are my uncles.

[chartsman]

What is the difference between strýci and strýcové?

[VladaFu]

No difference here. "strýci" can also be dative singular, but not here.

[Paul378887]

Why not “Matěj a SVEHO bratr...”

[JBHayven]

Because "svého" refers to the subject (it means exactly that: "the subject's") so it cannot be a part of the subject phrase.