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/
cooking.stackexchange.com/users/3203/TFD
I could not find any credible sources indicating that flax seeds (also known as linseed) lose significant nutritional benefits after they've been smashed, crushed or ground.
This article from Mayo Clinic in fact indicates that since the seeds tend to pass undigested, it is better to grind them: Most nutrition experts recommend ground flaxseed because your body is better able to digest it.
Whole flaxseed may pass through your intestine undigested, which means you won't get all the health benefits.
cooking.stackexchange.com/users/14401/SAJ14SAJ
I was told by a nutritionist to eat flax seed.
If eaten whole, the seeds simply pass through the digestive system without contributing anything; they have to be ground in order to reveal their properties.
As ground flax seed has anti-oxidative properties, it goes without saying that exposure to air reduces these properties thus the ground seed should be eaten as soon as possible.
Whilst I buy whole flax seed once every five or six weeks (about a kilo and a half), I grind only enough to be eaten in a week.
I've never noticed any taste to the seeds, let alone any rancidity.
cooking.stackexchange.com/users/3469/No'am Newman
Flax can go bad within a few weeks after it's ground Ground flaxseeds "can start to go rancid fairly quickly — as soon as a few weeks after they are ground.
This is when the fats start to oxidize, and ... is when you can also lose the nutritional benefits of those fats.
The taste is also off."
(Source.)
Unfortunately, if you buy ground flax from a store, there's a chance that it might be more than a few weeks old.
Still, please read on.
Buying refrigerated or vacuum-packed ground flaxseed
"Ground flaxseeds are usually available both refrigerated and non-refrigerated.
If you are purchasing ground flaxseed that is sitting on the store shelf at room temperature, we recommend that the flaxseed be packaged in a gas-flushed, vacuum-sealed bag.
If you are purchasing ground flaxseed that is found in the refrigerator section, it's not essential that vacuum-sealed packaging be used".
(Source.)
Once you open a vacuum-sealed bag of flax, air will enter.
Once this happens, it's wise to refrigerate or freeze the product.
Finding vacuum-packed flaxseed in your region
You can do a Google search for [ buy vacuum-packed flaxseed ] to look for companies in your region who manufacture the stuff.
I live in Canada.
Here: CanMar produces various "Fee Fi Fo Flax" and "Flax For Nutrition" vacuum-packed roasted flax products.
These products cost about 5 to 9 CAD per pound, depending where you buy them.
The company states that unopened packages will stay fresh for 18 months.
Puresource produces "Inari" brand vacuum-packed ground flax.
It costs about 7 CAD per pound.
Storing and taste-testing your ground flax Once you have your ground flax, it's wise to always refrigerate or freeze it.
"Because ground flaxseed flows readily even when frozen, many users choose to store ground flaxseed in the freezer for even longer shelf life." (Source.)
You can take a spoonful of your ground flax and taste it.
If it tastes good, it's probably still fine.
If it tastes bitter, fishy, or rancid, it may be best to throw it away.
cooking.stackexchange.com/users/21070/unforgettableidSupportsMonica
In my reading of the question, what is being asked is whether we can buy ground flaxseed, (or, alternatively, whether it is necessary to grind flaxseed within four hours of consuming it.)
SAJ14SAJ's answer confirms that it is advisable to consume ground, not whole, flaxseed, since otherwise flaxseed passes through the digestive system intact.
It does not address whether the grinding must be done just before consumption.
According to references such as this (excerpt: " The low levels of FFA and conjugated diene indicate that ALA remained stable during processing and cooking of spaghetti fortified with ground flaxseed.
")
it appears we can have confidence that it's all right to buy ground flaxseed, just so long as we use it reasonably quickly.
Additional references are welcome.
The main difficulty of grinding flaxseed at home is that the shell is not just tough for the human digestive enzymes, it is also tough for ordinary coffee grinders.
A grinder suitable for espresso or Turkish grinds is likely necessary.
Those are frequently called "Burr" grinders.
They are easy to identify (aside from the price tag).
They move the material from one compartment to another.
They do not grind "in-place".
Related Q & A
cooking.stackexchange.com/users/41295/Calaf
I am from Santiago, Chile. Here, there's a rumour that smashed (ground) flax seed loses its properties in around 4 hours. Do you know anything about this?  Basically, the rumors say that the flax seed loses its nutritional properties, and that it can even be unhealthy once it is ground — but, if you grind it yourself and eat it right away, it's OK.
Does flax seed lose its nutritional properties after it's ground up?
cooking.stackexchange.com
<storage-lifetime><storage><seeds><grinding><flax>
cooking.stackexchange.com/questions/29481
cooking.stackexchange.com/users/14924/Néstor
While seeds that have been ground  or otherwise processed will lose flavour and nutrition and go rancid, this is likely to take place over weeks rather than hours. Seeds that are ground will start to lose nutritional properties. They will keep for a few weeks without going rancid.
Seeds that are ground and exposed to air will lose nutritional properties. They will start to go rancid after about 4 weeks. Four hours is to short, it should take a few weeks before anything happens.