Can your next life be in the past?

There is no flaw if time doesn't exist in the afterlife.

Time doesn't exist now. The past was, and future will be. "Now" always exists, but matter makes it seem that what was and what will be are actual.

Every letter typed so far in this post, the second I finish typing it, is an event that no longer exists. My typing each letter is a past event, every letter I'm about to type is a potential event, and the moment I hit submit, it all will be lost to the past. Where are these moments? They don't exist. Only evidence of these past moments exist, right now.

Your next life will be like your 'now' life. The same, existing in 'now', not the non-existent past, or the non-existent future. Perhaps there will be material evidence that makes you believe the past is existing, but most people understand the afterlife to be an existence free of matter, and therefore, free of illusions.

If time doesn't exist, there is no way to choose an earlier time period.

Yes but only if time and space mean the same thing when looking at the universe.

Time is fake, we are in a cycle of infinity and beyond. Of course you can always work toward spiritual enlightenment and leave these cycle.

Marty McFly's was for a wee bit.