I'm reasonably sure that flash for Maxthon 3 has to be installed in a particular way with part of the installation involving copying and pasting a file into Maxthons plugins folder. If you have Max 3 I'll give you more info on this. (Thanks to mnshiner).
Maxthon 4 may involve a similar process but I don't have that version anymore and I can't remember.
Maxthon 5 probably just updates flash the same as every other browser these days as it's a modern version.
Flash has to be removed correctly to ensure the following re-installation isn't corrupted by left over bits from the previous installation. See here.