You'll need to create a .flash file. The file consists of the sound effect that plays, the voices that play, and the text category and entries in your .lang file (for the subtitles). Here's an example from the cistern in TTD:
<Flashback>
<Voices>
<Voice VoiceSound="flashbacks/CH02L18_CisternVisitbs_01.ogg" EffectSound="fb_sfx_18_cistern_visit.ogg" TextCat="" TextEntry="" />
<Voice VoiceSound="flashbacks/CH02L18_CisternVisit_01.ogg" EffectSound="" TextCat="Flashbacks" TextEntry="CH02L18_CisternVisit_01" />
<Voice VoiceSound="flashbacks/CH02L18_CisternVisit_02.ogg" EffectSound="" TextCat="Flashbacks" TextEntry="CH02L18_CisternVisit_02" />
<Voice VoiceSound="flashbacks/CH02L18_CisternVisit_03.ogg" EffectSound="" TextCat="Flashbacks" TextEntry="CH02L18_CisternVisit_03" />
<Voice VoiceSound="flashbacks/CH02L18_CisternVisit_04.ogg" EffectSound="" TextCat="Flashbacks" TextEntry="CH02L18_CisternVisit_04" />
<Voice VoiceSound="flashbacks/CH02L18_CisternVisit_05.ogg" EffectSound="" TextCat="Flashbacks" TextEntry="CH02L18_CisternVisit_05" />
<Voice VoiceSound="flashbacks/CH02L18_CisternVisit_06.ogg" EffectSound="" TextCat="Flashbacks" TextEntry="CH02L18_CisternVisit_06" />
<Voice VoiceSound="flashbacks/CH02L18_CisternVisitas_06.ogg" EffectSound="" TextCat="" TextEntry="" />
</Voices>
</Flashback>
In the level editor, add a Flashback Area, then go to the area properties, click the [...], and select your .flash file. The flashback sequence will start when the player enters the area.