is there an official store for buying nasa patches?

My question is: how much to get my own?

Not really design … just manufacture. Design is usually done in-house as far as I know

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They have an online shop too, big selection of patches, I recommend them if you collect patches and need a place to buy some

All bigger official NASA websites/centers usually have their own store,

there is shop NASA, which is JSC based.

Thespaceshop, which is KSC based.

The best IMO is direct from the vendor itself at space.abemblem

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KSC - Kennedy Space Center

JSC - Johnson Space Center

For those ... spacing out.