(Not a teacher)
'Barking' is in progressive/continuous form.
'Kept' is a catenative verb, and these verbs are always followed by either the 'to infinitive', past participle, or progressive/continous form. Not all of them can take all these forms.
When a verb phrase has more than one verb, the only the first verb in the phrase takes the tense marking. The other verbs are finite - no tense.
Student or Learner