Well, there's two ways of looking at it. From what I understand, sundew flowers don't zap the strength from the plant like flytrap flower stalks do. But, if you wanted to start new plants from the stalks I would think it'd be about the same as for flytraps...cut into 1" to 1-1/2" sections, if they're lengthy. The best chance of producing new plants is with young stalks...maybe 2-3 inches long. Water propagation should work or sticking them end-first down into some sphagnum moss, either dried or live moss. I've had my best results from using live moss. Starting from cuttings (leaf, stalk, pullings, etc) is "vegetative" propagation as opposed to propagation by seeds. You get fewer plants from cuttings but you get plantlets that get big faster, usually stronger, and are identical clones of the mother plant.
The alternate option to taking flower stalk cuttings would be to let the flowers grow, be pollinated, and produce lots of seeds. Some types of plants can be "seedy" in that they produce and scatter seeds around their pots into other plants' pots. You have the possibility of created tons of seedlings...if you need tons. Also, the subsequent seedlings can have characteristics of plants many generations in the past, even to the point of looking very different from the mother plant...the seedlings will not be clones of the mother.
So, it's not necessary to cut the flower stalks unless you just want to. To cut or not to cut...that is the question. Wait, no it's not
, it's "...when's the best time to cut the stem?". I'd say when the stalks probably anywhere from 1-3'ish inches tall. Once the stalk gets older the chances of "striking" goes down.
I'm basically a rank newbie that likes to run his mouth so take all of the above with a pinch of salt.
Maybe there's something there that you can use, though.
Best wishes on what you decide and if you do take cuttings on them striking nicely for you!