The kindergarteners were walking through the park holding hands.
Literal
Kindergarten-children [topic-は] hand [object-を] join-[and-て] park [possessive-の] inside [through-を] was-walking.
手をつなぐ ('join hands / hold hands') is a fixed expression — つなぐ means 'connect / join.' ~を歩く uses を with a motion verb to mark the path being traversed (cf. を with motion verbs like 通る, 渡る). 幼稚園児 ('kindergartener') is a compound 幼稚園 ('kindergarten') + 児 ('child').