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I'm not sure. I will try to do just a guess:
I think the same flies that survive in deserts... Culicidae?? Stratiomyidae...
Really, like you, I want to know what dipters can survive a lot of time with very tiny quantities of water! - it is your question. ;) But those flies I suspect that can benefit of more drier weather...

I know for example, that salticid spiders, (some) has great capacity to survive in very dry conditions. One example really true: I forgot one salticid inside a car - Philaeus chrysops (very beautiful indeed) - that survived during more 4 hours with almost 70?C inside! Very impressive! There are much more salticids with spectacular records concerning live with very, very small quantity of water and very dry habitats.
Of course, there are deserts that aren?t dry. :P Like Antarctica.
Look... another question arise! Which kind of dipters we can find in Antarctica?

Another example (but in extreme opposite).... the famous Araneus diadematus can survive(if temperature decrease slowly) until -30 ?C! Life is more fantastic that we usually think! ;)

Sorry, if I talk about "no dipters"... but everything is in relation! There are many spiders that consume dipters, and some dipters that parasite spiders. ;)


Below follows an image of Philaeus chrysops to get an idea: