DIAGNOSIS Stop using the desk immediately. A burning smell indicates an electrical fault, most likely an overheating motor or a short in the wiring. This is a potential fire hazard and a serious warranty issue.
FIX 1) Unplug the desk from the wall right now. 2) Do not attempt to use it again. 3) You need to identify the source. After it's cooled down (wait an hour), carefully sniff near each motor column and the control box. The faulty component will have the strongest odor. 4) Contact FlexiSpot support immediately. Have your order number ready. Describe the burning smell and which component it's coming from. They will arrange for a replacement motor column or control box.
IF THAT DIDN'T WORK If the smell is very faint and only occurred once after prolonged heavy use (like raising a massively overloaded desk), it *might* have been overheating protection kicking in. However, you should still treat it as a fault. The desk's motors should not produce that smell under any normal operating conditions.
HEADS UP This is not a 'wait and see' problem. Do not plug the desk back in to 'test' it. You risk further damage, voiding your warranty, or creating a real safety issue. Let the company handle it—this is exactly what the warranty is for.