Most families who homeschool or worldschool abroad get the teaching part right and the record keeping part badly wrong. It rarely matters until it suddenly does.
The moment it matters is enrolment. You decide to put your child into a local international school, or you move back to your home country, or your visa situation changes and you need a school place quickly. The school asks what your child has covered and to what standard. If your answer is a shrug and a folder of nice photos, you are now negotiating from a weak position with someone who has other applicants.
This comes up regularly with parents in the TDY community. Phuket has decent international school options, but places are competitive and admissions teams want evidence, not enthusiasm.
What to keep is less than you think. A simple term by term log of subjects covered. Sample work, a few pieces per subject, dated. Any assessments, even informal ones. A reading list. If you use an online curriculum, export the completion records rather than assuming the platform will still exist in three years.
Do it monthly and it takes twenty minutes. Do it retroactively and it takes a weekend of guessing.
The wider point applies beyond paperwork. Nomadic education gives kids things a classroom cannot: language exposure, adaptability, real world problem solving with actual consequences. Those are genuine advantages. But they are hard to demonstrate to an admissions officer, and the burden of proof sits with you, not with the school.
Keep the records boring, current, and portable. It is the least interesting part of educating your kids abroad, and the part that protects every other choice you have made.