Mary is a Witch! She was able to fly in the very last scene without the Fly By Night, and was able to fly strong well after her magic failed her when she lost the flower and book to Madam Mumblechook. Much earlier in the movie Mumblechook commented that her red hair and familiar meant she was a powerful Witch, and she was right! In the end credits sequence we see a picture of her whole family, including Mary's parents. They are respectively blond and black-haired. It's very unlikely those two would produce a redhead, given that we know that Charlotte also had black hair, signifying a stronger genetic predilection for that. So what? Well, Charlotte had red hair too! Magic gave her hair color before she lost it, meaning that it's possible that that's the source of the color of Mary's hair as well. So her being able to fly her broom during the ending, plus the power of genetics... well, it's likely Mary isn't quite done with the magical world just yet.
Or, more precisely, the contrary. In the second part of the movie, Madame Mumblechook and Dr. Dee want to experiment on Peter, and this is a totally illogical course of action, because:
They have a very limited amount of the magic flower, and, also in a case of success, they might not be able to repeat it; the better thing would be to grow a field of such flowers before any experiment;
In case of success, they would have given enormous magical powers to a boy that see them as enemies; (the first experiment, seen in a flashback, was probably on a volunteer).
Peter is a random Muggle. If you want to make a supremely magical being, surely is makes sense to start with someone who has some magic already? Not to mention that their stated goal is making their students into better witches and warlocks.
Madame Mumblechook gave her word to free Peter in exchange for the flower, yet she did not follow on it. Traditionally, magic is linked also to words, and this is Laser-Guided Karma, too (she did not even make the effort to find a loophole): for a wizard, the risk is to lose the magic. Well, this happens but for other causes.
The magic flower only blooms every seven years which may explain why Madame Mumblechook and Dr Dee were in such a rush as they very probably did not want to wait seven years (they had already waited long enough between the previous attempt and their current one). It doesn't explain their other illogical choices, unless we assume they're going senile.
Their first experiment used a willing magical student and the magic went wildly out of control; it's possible they thought using someone completely unmagical might make the process less likely to go wild, and after it succeeded, they could study him to learn how the process functioned and if there was a safe way to adapt it for magical individuals. Also, it does seem like the two of them have lost the plot, as they're seemingly unaware of how evil they've become. They appear to think the nonmagical animals they've transformed are better off; they might not be able to comprehend that Peter wouldn't want this transformation once it succeeded. Despite antagonizing Mary, they do show concern for her and Peter once the experiment goes out of control. Aunt Charlotte at one point comments that the madame and doctor were once good and intelligent people but greed for power changed them, and this greed could have made them less careful in their methods.
