if you make your own chassis do you have to have it tested for strength/flex etc by an external company?

No!

But, the SVA tester will have to be satisfied that it is strong enough and up to the job.

So take lots of pictures etc and document everything!

So that when the tester asks why you have put tube X in a specific place you know and can basically presuade the tester that you know enough shiz to have done a proper job..

If it looks right, it usually is!

Build a balsa wood scale model of your chassis. Take the model along to the test and physically demonstrate how stiff it is to the tester if he questions the design.