If you don’t want to use any FXs…
You could transition to the ‘flash back clip(s)’ through white and make the ‘flash backs’ look like old-early footage by either reducing the colour saturation / adding noise / vignetting / etc – depending on how far back in time and/or the emotional connection of the ‘flash back’ to the subject.
Or you could use two black (dark orange/brown) solids and animate them to look like someone shutting their eyes and increasing blur to the ‘transition’ then fade to the ‘flash-back’ clip.
Or you could focus in on the subject’s face and fade to ‘flash-back’.
If you want to use audio to emphasize the fact that you are returning to the past… you could gradually add echo / reverb to the subject’s words that cue the flash-back…
Hope the ideas help – but, of course, there is no better way than to analyse what the pro’s do and adapt to your particular need…