OP I work in Supply Chain. No expert, but my thoughts are..
There is a risk to aviation although personally I think this would be sorted prior to a No Deal. There could be an indirect impact due to overload on UK customs / ports until the required infrastructure (resources, systems etc) is put in place to deal with road freight from Europe.
Of course we will still be able to buy products from Europe - we actually have to, otherwise pretty much every single sector of manufacture in this country will grind to a halt, not to mention healthcare and other public services
. Things may take longer to get here and cost more.
Unless they've done it already, there is probably not enough time between now and March for manufacturers to move to suppliers outside the EU for raw materials, and until the outcome of the deal (or not) is known, businesses would be unlikely to make this move anyway, so UK manufactured foods and other consumer goods are highly likely to be impacted by a No Deal outcome.
I don't know much about retail so I don't know how easy it would be for the big retailers to switch from an EU supplier to a non-EU source, but you've got to consider the scale at which this might need to be happening - if all the retailers suddenly want to buy all of product X from the US rather than EU, it's not going to happen quickly.
I do think delays in the Supply Chain could lead to short term unavailability, especially for basic items which people are most likely to stockpile / panic buy. Take bread, for e.g. If UK bakeries face delays in getting their bakers yeast from France, there could be a shortage of bread. As soon as people realise this, they will panic buy, and there will be no bread available. When consumers stockpile, and manufacturers are trying to match increased demand with lower output, situations can get really entrenched, and shortage of supply can go on for a lot longer than the raw material shortage lasts for.
I will certainly be doing some "prepping" if we have no deal by the end of the year and I am not given to prepping usually.