Does flax seed lose its nutritional properties after it's ground up?
Any seed that has been damaged, cut, smashed, milled, or ground starts to lose flavour, texture, nutrition, and eventually will go rancid due to oxidising oils.

Four hours is too short a time for anything noticeable to happen. Some types of nuts and seeds show a noticeable change over a day or two, but most take many days or weeks.

Milled flax seed is reasonably tough; it should last for a week or so without a noticeable flavour change, and many weeks before going rancid. For more information and sources, please see: https://www.goldenvalleyflax.com/flax-facts/health-research-articles/flaxseed-storage-baking-stability/