If I'm understanding this correctly were denied the sale because of a NICS background check that was performed at Walmart. Now you want to buy a gun online and avoid having it shipped to an FFL? That's not possible. The FFL will do exactly the same NICS check Walmart would do.
You cannot avoid having it sent to an FFL. Trying to do so is illegal in itself. If you feel there is any way you could be denied from a dealer then trying to purchase from a private party without a check is also illegal.
I would suggest that if your state allows for it to get a firearm purchase permit or concealed carry permit. If you go through that process, the State or County or Municipality will do the background check. Then you show the store or FFL your permit when you fill out the ATF form 4473 at the time of purchase. If you don't have that you will be subject to a NICS background check each time you purchase.
You can request to appeal a firearm background check if you're denied. Use this link.
FBI Forms — NICS Appeal Request Form
More useful information for your situation at
NICS Appeals — FBI