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Let the leaves grow until its time to lift the bulbs for the winter. The leaves will supply nutrients to be stored in the bulb for next year's growth. Here's more information: https://www.gardeningknowhow.com/ornamental/bulbs/peruvian-lily/growing-peruvian-lilies.htm

The flower is Peruvian Lily or called Alstroemeria.
Enjoy!

https://www.gardeningknowhow.com/ornamental/bulbs/peruvian-lily/growing-peruvian-lilies.htm

Though these plants need fertilizer, make sure the application is a balanced formula.
Excess nitrogen can inhibit flower.
Try adding some phosphorous to promote flowering.
Bone Meal is a good way to do this.

https://www.gardeningknowhow.com/ornamental/bulbs/peruvian-lily/growing-peruvian-lilies.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/bone-meal-fertilizer.htm

The answer will depend on the seed kit you have purchased. Peruvian lily seeds need to be stratified, a procedure involving exposure to cold temperatures over specific periods of time, and then scarred in order to germinate.

If the seeds you purchased have already been prepared in this way, you can plant them outdoors at any time in your zone. The seeds can then take up to a month to germinate.

If they have not been stratified, you will need to go through this time-consuming procedure yourself.

This issue can have a few different causes. They can fail to flower because of, either, too much nitrogen or not enough phosphorus and potassium. Adding the latter two will help offset the nitrogen, and will likely fix the problem.

Too compact of soil can also cause this, however. This will require digging them all up during dormancy, and tilling the soil while adding in materials to improve drainage before planting again.

If you can't fine them locally; do a Google search for mail order sources.
Also try Etsy and Ebay, they are often good sources for bulbs!