It depends on what your homing missiles are homing in on: Iron Man and others seem to mostly destroy/hit real estate or swooping (=bird-speed) targets hundreds of meters away. If your target is of that ilk, the launch is no big problem, a burst of compressed air forcing the missiles out and up, where the missiles then fire their puny main drive to accelerate to/stay at the new-year's-rocket-speeds (~100m/s = 1/3 Mach) that are the still-visible-but-blurred mainstay of cinematic combat. Missile reaches their target at 100m distance after a leisurely second or two. Neither the initial launch, nor the main thruster will output reactive forces that endanger anything nearby - 100g rocket, pencil size, accelerated to 100m/s over the depth of a chest cavity (25cm): v²/2l = 2000G, or in other words, 200kg sitting (not hitting!, just sitting) on the chest of your war robot. That should be within war-robot specs. This all is dependent on the missiles not being very fast - but if the homing mechanism is good, they do not need to be, for quasi-static targets.
To intercept missiles that themselves race at 1000-5000 m/s or similar tasks, the involved accelerations need to be far more drastic, of course. Also, for far-away targets it might pay to be a bit more swift, as the traveltime of the missile may be used by the target to seek cover. Short duration-to-target also means high velocity (aerodynamic drag is dependent on velocity squared, so that is bad), which in turn begs high acceleration, which needs bigger distance to main engine firing (for safety), which needs high initial acceleration, which means explosives, lots of kickback, etc.
Most mini seeker missiles in movies are displayed at low(missile-wise) speeds, though: Running typically makes a real difference in when and how they hit, which means that their speed is not many orders of magnitude above that of a runner, so i guess as long as you play tho the cineastically mided, you are fine with a honeycomb of missile silos in the chest.
Scaling down a missile alters several key dependencies: Smaller size means lower Reynolds numbers, which is bad for aerodynamics (at same speed as big missile). Smaller size means less volume (=propellant) per unit surface (drag), meaning worse long-distance performance (a 1/10th size missile has 1/1000th of the propellant but still only 1/100th of the aspect area of the 1/1 missile, thus it will not go 1/10th of the way of the 1/1 missile, but much less.). At the same time, most engineering-relevant values for performance of structural materials go up when scaling down, so you'll get away with relativly thinner structures (this does not make up for the propellant-problem, though). Surface-to-volume also rules the interactions of any lifting/steering surfaces, so you may get better dodging and weaving as long as you handwave the performance of the neccessary servos.
Your chest fired homing missiles will probably be cool gadgets. Keep in mind that the payload of a missile is about 5-10% of the whole missile's mass, so keep your expectations of efficacy low. 5grams of ONC still can deliver about 10kJ, but while that can easily kill an unarmored human, it will just tickle armored targets. Possibly better to go for more specific goals, i.e. deliver trackers, disable optics/radar.
- Use the a=v²/2l formula (or rearranged version) to calculate on the dependency of acceleration (a), resultant velocity (v), and available acceleration-length (l).
- Use F=m*a (or rearranged version) to calculate on the dependency of force used (F), mass accelerated (m) and acceleration achieved (a).
(1) will also be interesting for the other aspect of homing missiles: Say the missile is travelling at 100m/s down a hallway, and now has a t-junction of 2 meters width coming up. It has to go right. This means that it's forward velocity will need to be reduced to 0, while it's sideways velocity will need to go up, all in the space of 2 meters (otherwise it will hit the wall). So (just the breaking, not counting the re-acceleration) will be done with (100m/s)²/2*2m = 2500m/s² (= 250G, i.e. 250 times earths gravitational acceleration). For a 50g rocket (it already lost some of it's original 100g mass in flight) this means the application of 0.05kg*2500m/s = 125Newton force, over 2 meters, meaning 125N*2m = 250Joule energy. Rocket Fuel has about 1MJ/kg, so that would be only 1/4gram expended (+1/4 gram for re-acceleration). Good hunting!