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It is unspecified whether you are driving LEDs as in plain LED components (some LED-strips are plain LED in series-parallel combinations, others are not) or LEDs as in LED appliances like MR16 socket based ones.
The latter include additional electronic circuitry (gosh, some even include fans!) usually not so happy to live on anything else than 12V sinewave or DC. This circuit usually does rectification, filtering, DC/DC conversion, etc. and provides a constant current source being the preferred method for driving LEDs.
Plain LEDs should be fine with a 40kHz supply. Appliances usually aren't happy. Flickering, out of spec temperature ranges, etc. can happen. For effects that can be observed, albeit for different reasons, and why or why not to use
legacy transformers, see halogen transformers for LED.
This 40kHz signal is very likely some sort of squarewave or other signal (the very short rise/fall time is the main culprit) which is a huge source of interference, even more so the more power is driven and the longer the wires. Unshielded 40kHz signals in 12V appliances could easily drive your amateur radio neighbour up the walls, the interference usually goes unfiltered and propagates easily so in the end your entire electrical installation constitutes a big antenna. Not to mention degrade your own AM radio reception. As noticed it also deeply disturbes the electronics inside your exhaust hood's lighting system. NB, similar situation arises with powerline-communication (PLC) which sometimes even is held responsible for avation-grade interference.
It is very easy to buy LED appliances even from local stores, name brand labeled and nonetheless they're produced overseas which in turn renders it quite likely that the circuitry inside -- being of high volume, low quality design and components -- is itself such a source of interference (the web is full of such references).
Plain LED parts (as opposed to LEDs with circuitry) are fine with 40kHz (they're all that often driven by PWM). Everything else i.e. surrounding electronics from other LED lights to amateur radio is rather turned off by 40kHz squarewave radio interferences.
Flickering: Either drive plain LED parts by current controlled plain DC or use appliances (with plain sinewave or DC). And those may provide their own switching frequency which are out of user control and it may happen they internally use 40kHz or something in that range, are effectively unfiltered and therefore constitute a source of interference themselves. Difference: It's the appliances 'fault' instead of user's decision. Pick your favourite, that being said the appliances seem the mass market's solution.
edit: @blablubbb's answer above includes a link visualizing some types of interference waveforms (aka noise).