(and I thought there were supposed to be EEs camping on this forum. I don't think I've heard from one)
There are several EEs on the forum, but they are possibly scratching their heads at the moment, deciding where to start!
There are a few issues with your circuit that need attention. Yes, you do need some series resistors with those LEDs, unless you are using the ones with integrated resistors.
Do you really need an ARM LED in series with a ‘Stand By’ LED?
You flashing module has two connections to ground or -V (one off to the left, and one from the + terminal). Can’t really comment on the flashing module adequately because I don’t know anything about it.
The 5th position of your upper pole of the rotary switch switches to ground or -V. Is that what you want to happen?
Do you really need two 12V 7Ah batteries? Probably a little overkill.
Your LED symbols are a little unusual! I’ve been in electronics for 40 years and haven’t seen that one used for a standard LED.
The ‘Checklist Complete’ and ‘Arm’ switches are redundant. I would just have the ARM. I would also bring the input side of the continuity switch to the input side of the ARM switch.
However, points for giving it a go! You’ll get there with help from the good folk here.