With the caveat that all this is dependent on whether or not the birth data is accurate ... and that this analysis is for fun and information only ...
I can see why Britney is going through so much right now. She's got strong Pluto contacts in her chart, messing with her natal Neptune which natally squares Mars. Translation from the Astrologese: Mars Square Neptune equals drug abuse. In her case, potentially fatal drug abuse or serious jail time (12th house Mars), if she does not find some way to reconnect with a spiritual or creative outlet. I hate to say it but right now the creative isn't working for her all that well, and fame isn't helping matters. Her only hope is a profound spiritual experience, a rock-bottom "near death" experience might be the life-saving experience she needs to wake her up. Losing custody of her kids hasn't seemed to make a profound impact, the possible loss of loved ones in other areas is featured in her transits right now. There could be a death in her family, and with what is known I truly fear for her own well-being, frankly.
Do Britney and Justin have a karmic connection? Yes, absolutely. Just because two people have a karmic connection does not mean they are "meant" to be together, or are even good together, though. Her Moon and his Sun are exactly conjunct, a strong sign of shared past lives. She feels like he thinks, and vice versa. Their Suns are sextile. They are natural friends who can talk all night long. Their creative interests are in harmony. But yikes, their combined chart is not harmonious for romance! They have a pile of planets in the fifth house, good for lovers, not so good for marriage partners. But those planets make hard aspects to the second house - an indication of arguments over money, finances and values. Venus and Mars ("she and he") make no aspects. No lasting mojo. And Moon Squares Saturn ... massive insecurity complex. These two would be competing with one another. I don't follow either of their careers, I only see what I see on CNN as it flashes by or hits me when I watch Larry King, but right now his transits show someone who is disillusioned with or burned out by his daily routine, someone undergoing a lot of emotional and mental changes, which may be painful but are part of "growing up". Britney seems determined to run away from responsibility right now. That doesn't bode well for a rekindled romance.
I know absolutely nothing about Jessica Claire Biel. And we don't have her birth time. The best I can do is a combined chart for her and Justin. It has a lovely grand trine with Moon, Uranus and North Node (translation - high profile partnership, highly creative, unusual with lots of twists, turns and surprises, most of them positive). They have escapist tendencies. No Mars-Venus connection here though, and Mars does hit Neptune, so this isn't the best match, either. Will they break up soon? Hard to say, but Justin isn't the best bet for settling down with anyone right now. Uranus is transiting his 7th house of committed relationships. It moves slowly and has a long-term effect. Forcing himself to "settle down" would be a big mistake for this young man right now, even though he may be pushed in that direction by the women in his life (Uranus opposes Venus at the moment). That Uranus-Venus opposition hits Jessica's Sun. Since I don't have a time, I can't tell if this will center around relationships, but it will have a transformative influence on her personality, especially how she sees herself as a woman.
You do have to keep in mind no astrological chart can tell you for sure exactly what choices a person can make. All three people have challenging aspects - and I have seen people overcome far worse. As an astrologer who has not been consulted directly by any of the parties, I can only say so much. I see that all of these folks live in a highly-charged world that the best of us would have a hard time understanding. To put it bluntly, they are not living in the real world, but who can blame them? I would not be so bold as to tell Mr. Timberlake what to do. But if he wants a real shot at transformation and growth, with a few challenging side-trips into painful territory, he'll stay with Jessica. If he decides he wants a really exciting wild ride filled with drug abuse, jealous rages, competition and dysfunction, he'll go back to Britney. Of course there is the possibility of neither, or of his finding someone new. Anything is possible.