If you're keg is carbed, and you're filling the bottles full (normal full, like 2 inches of air in the neck), and you're capping them tight...you should not have the carb vanishing, ever. I drop the pressure in my keg to 5psi or so, purge it and drop pressure I should say, and put a sanitized bottle directly on the tap, at an angle, pull the tap and done. Cap it as normal, good to go for weeks or months on end, never an issue.
Avoid foaming at all costs as it just wastes beer and takes up precious room, which reduces the carb once it dies down and equalizes. Chill the bottles in advance to help that, if needbe.