I'm a hobbyist but here's my view on the matter:
Using a transformer to match up to the very low impedance of your squib may seem like a good idea (and it is), but ignoring the details of your primary circuit for a moment (it's not relevant to me for now) the problem will be in transferring sufficient energy to guarantee an all-fire specification for your squib.
You've provided zero specifications for the squib. Estes provides very clear all-fire specifications for their rocket engine squibs, by comparison. You have to deliver a certain number of Joules (about \$\frac{1}{2}\:\ J\$) within a certain period of time (\$50\:\textrm{ms}\$) in order to meet their all-fire specification. Their specification is actually rather difficult to meet with a transformer arranged as you have it.
Review this answer I provided earlier regarding the basic energy equations for capacitors and inductors.
A capacitor's energy is \$\frac{1}{2} C V^2\$ and is stored as lines of electric force in vacuum regardless of the dielectric itself (which actually acts to counter the electric force in dielectrics), but it's easiest to imagine that once you've selected your capacitor the energy present is a matter of how much charge stored on it. Matching up the capacitor to a particular squib would be about meeting the specification I mentioned earlier. You could store a lot of energy on a super-cap, for example, with very low voltage. But it wouldn't deliver the required energy in the required time since the voltage present would be too low to induce enough current in a short enough time. Most of the energy would stay on the capacitor. So the selection of the capacitor depends upon the load. The pairing must be arranged to meet the all-fire specification.
An inductor's (transformer here) energy is \$\frac{1}{2} L I^2\$ and is stored as lines of magnetic force in vacuum space regardless of the core material used. (In your case, you may want a gapped core.) But again, it is easiest to imagine that once you've selected your inductor/transformer, the energy present is a matter of Webers (volt-seconds, and the equivalent of charge on capacitors.) Again, the selection of the inductor/transformer depends upon the load and the pairing must be arranged to meet the all-fire specification.
For inductors/transformers this is often more of a problem. You may have noticed that the volume of a capacitor (for a given manufacturing technology) is proportional to the energy it can store. The same is true for inductors/transformers.
If you had a specification (you don't, yet), it might be possible to compute the required core volume needed to store the energy you want held there. (You might read this post from me which is one place where I discussed core volumes.) But that can't be done just yet because you don't have a specification. And I suspect you will be disappointed at the sheer size required, once you are able to provide an accurate specification (considering that you are imagining a single pulse here.)