Perhaps someone will come along who knows whether certain rail joiners will work.
If you have any kind of rail joiners you could try them and see. As long as both track brands are nickel silver they should solder together fine. I would make a strip of wood about an 1/8th inch thick...nine millimeters wide (to fit between the rails) and at least a foot or more long. Use the wood strip between the rails to align one straight section of unitrack with a straight section of atlas flex (no curves) and clamp to hold in place. Rig it somehow so the top of the mating rail sections are the same height. If you can get ten millimeters of both rails on the ends of each track section free of any ties.....and ready to butt together....you should be able to pry open whatever rail joiners you have.....and at least get them to slide over the ends of both tracks loosely......then after you're sure all is well aligned...use flux paste and solder the sections together. If, after soldering, the tops of the rail joints are slightly misaligned you can carefully file them flat using a jewelers or fine file.
This is how I would do it anyway. It would be easy if certain rail joiners worked perfectly......but soldering is a better long term solution.
Mike