You can but producing onion seed is not straight forward and probably not worth the effort for you.
They are biennials so it will take you two years to produce seed. The first year the plant will produce a bulb as usual and the tops will die back, then you must select for the type of bulb characteristics you want and then save these bulbs over the winter in the right temp and humidity. Then you replant these bulbs the following spring and they will bolt and be allowed to cross pollinate via flies. The catch is that if you let only a few bulbs goto seed this will cause a bottleneck in the genetic expression of the onion and cause something called inbreeding depression. You need at least 50 plants bolting in a block to encourage as much cross pollination between as many plants as possible to preserve genetic heterogeneity. This is because onions are outbreeders and any inbreeding causes drastic and permanent loss in vigour, this is exaggerated with every successive generation.

Hope this helps

-Ken

To make your own seeds is simple: plant the normal onion
(early spring). It will eventuall flower and produce seeds.
Dry the seeds well and keep in airtight container in refrigerator.
CAUTION: You want to produce seeds from onion that is righr for your latitude.For example, in south Georgia you need SHORT DAY onions, in WISCONSIN long day kind.
Therefore, if you plant your own hom grown onion, you can be sure that you will get the right kind of seeds.