As you compare SET to bitflag, I guess you want to store the state of all the checkboxes in one record.
Simple math suggests that if you have 64 checkboxes, you have 264 possible combinations of checkboxes.
A SET type can only have 64 members, so you'd need a few (2.88E17) columns to have enough members.
BIGINT is 63bit signed, and the manual warns not to use unsigned values because the 64th bit might be mis-interpreted.
Another way to store the data would be to create one big table and store the data of each checkbox in it, along with data about who the record belongs to (userid etc).
That does give you one heck of a lot of records, but they are perfectly indexable, so speed is hardly an issue.