Here is a photo of my P. chilensis. You can see some seedlings, that are likely from a seed pod which I forgot to harvest. One of the amazing traits of this plant is that it is completely autogamous!
The flowers of P. chilensis are very short, the stalk can be sessile like mine, or a few cm long. The flowers are often covered by the leaves of the plant, as P. chilensis grows very fast for me (I have not measured the exact amount of time, but I expect it is about a new leaf around every 6 days). Flowering for P. chilensis seems to be associated with water level. When I came back from vacation (I left it in a few inches of water as opposed to a few centimeters) I found three flowers coming up.
You can also see a division under the leaves of the flowering plant. This plant is closely related to P. antarctica, so I expect it produces a short stolon, in a similar matter to P. antarctica, to produce new plantlets.
So far, this is a very easy Pinguicula species to grow. I grow it indoors under a seasonal light cycle (one you would give to tuberous sundews). I increase the photoperiod to about 14 hours during the summer. During the winter, I will reduce it to around 7 or 8 hours. This Pinguicula is homophyllous, but according to a Chilean native flora website, it can experience snowfall during the winter. I may try growing a few individuals outdoors this winter, since I have some seedlings popping up in another pot.
I have not tried growing P. chilensis outside during the summer. Well, I tried with one sickly individual, but it ended up dying. The main cause seemed to be fungus gnat larvae. I assume that the extreme summer heat weakened the plant to the point where the fungus gnats finished off the plant (it was almost dead indoors anyways). I may try to grow a healthy plant outdoors next summer. The sickly individual actually grew a few leaves while it was outside, so perhaps it is resistant to higher temperatures than it experiences in the wild (according to a website that has records of the temps where P. chilensis grows, the maximum summer tempurature is 78 degrees fahrenheit). It experienced temps in the 80s and occasionally high 90s while it was outside.
I have read that P. chilensis has not done well for someone trying to grow it under artificial light, but so far I have not had any issues. This plants seems to appreciate being fed, however, so if their plant was not catching prey, it is possible that this would be the source of their indoor-troubles. Whenever I haven't seen an small flies on my P. chilensis, I give them a light soaking of maxsea. The dilution I use is 1/4 tsp per gallon.
The most beautiful aspect of this plant, as well as its cousin P. antarctica, is the beautiful veiniation on the leaves. Enjoy!