TLDR; Guided missiles would still be possible as would fighter jets without integrated circuit technology it would just be much less efficient than those made today.
By chip I'm assuming you mean integrated circuits, which is where all components are placed within the same semiconducting wafer. I see no reason why you couldn't design semiconductors to handle high voltages, this requirement is not built into today's designs because it is not an issue. The current goal of modern IC technology is to get things as small as possible, not as robust as possible for which you would have to sacrifice a lot of size. For example field effect transistors can be made to with stand pretty high voltages if you want, the only problem is that the commonplace MOSFETs aren't designed with these restrictions in mind. In-spite of this there are many examples of MOSFETs for sale which can handle thousands of Volts; just google search power MOSFETs for instance. Of course these are still semiconductors and could conceivable be integrated with other components, I have not seen it done but this is only because we have no reason to, not because it is impossible.
This aside, using only vacuum tube technology actually comes at a disadvantage because triodes (which act like transistors) are actually less robust than Field effect transistors. For diodes, vacuum tubes are more robust on average, but this is only because of the application for semiconducting diodes.
If on the other-hand, you want to forgo any solid-state device altogether for the sake of the story, the earliest missiles were developed in the 1940s using only the simplest of circuits with the crucial component being the photo-resistor. While not created with any semi-conducting technology, the missiles essentially functioned similar to those today. The only advantage modern day air-to-air missiles possess of those of their predecessors is that they have much more advanced circuitry and thus can handle a much wider range of scenarios, but the underlying principles have not changed too drastically.
To get a good idea of what is possible without heavily reliance on IC technology, most of the technology deployed in the 1950s did not use solid state devices, particularly look at the early soviet aerospace and space programs, which even into the 60s and 70s tended to be very advanced but using less modern IC technology when compared to their western counter parts