Here is the flag of Norway. You can cut out rectangular non-overlapping regions from this flag to form flags of other countries. What is the most number of different country flags you can make?
We can make
up to 9 flags!
We have 6 starting flags: Indonesia, France, Poland, Finland, Netherlands and Thailand.
Ignoring differences in shading, Monaco and Luxembourg can be added, and ignoring symbols then Malta can also be added for a total of 9!
It's known as the Mother of all Flags for a reason!
The question says "cut out rectangular non-overlapping regions from this flag to form flags". Read literally, it suggests we are allowed to form flags from rectangular regions, not necessarily that the rectangular regions that are cut out must themselves be flags. If one permits reconstruction of flags from rectangular pieces cut out of the flag, I can get:
Directly stealing from BeastlyGerbil's answer, Malta, Monaco, Indonesia and Poland all require just one rectangle. I split France, Netherlands, Luxembourg and Thailand across several rectangles to address proportion issues, and Finland splits into four sections for the same reason. We also get to add:
Peru (2 sections, horizontally placed)
Austria (2 sections, vertically placed)
Russia (2 sections, vertically placed)
Costa Rica (4 sections, vertically placed; the blue splits in two parts)
Denmark (4 sections, on the corners)
Tonga, Switzerland and Iceland are a bit of a mess, but hopefully clear from the diagram.
There remains a legit question about shades of blue, as (say) the blue in the Russian flag is substantially lighter than that of Norway. But I have addressed all proportion issues: flags are constructed proportionally with the best information I could find with casual Internet searching (mostly Wikipedia).