I am not sure exactly what your problem is. Are you interested in a reaction with the maximum yield products per input masses, a stoichiometric problem or are you asking about a kinetic matter: how to speed the reaction up?

For the stoichiometric problem:
The reaction between citric acid and baking soda is:

C₆H₈O₇ +3NaHCO₃===>Na₃C₆H₅O₇ + 3H₂O+ 3CO₂

So to maximize the yield of CO₂ gas (since this is the gas produced and I imagine you are interested in the dramatics!) you should use one mole of citric acid and three moles of baking soda.

These mole numbers can be converted to mass using molecular weights. For baking soda its 84 g/mole and for citric acid its 192 g/mol (roughly).

So the ratio you want to use is 3:1 or 252/192 = 1.31. That is for every 1 gram of citric acid use 1.3 g of baking soda. This will give you the maximum amount of CO₂.

Then, for example, if you use, say, 25 g of citric then mix that with 32.8 g of baking soda . This will generate 0.39 moles of CO₂ or 0.39 moles X 44g/mol = 17.2g of CO₂ gas.

You can use the ideal gas law to determine what the VOLUME of CO₂ gas will be. After all, the bigger the volume the more dramatic the effect, right?

So P V = n R T and you have P = 10⁵ Pa, T = 298 K, R = 8.314 (SI units), and n = 0.39 moles.

Then V = 0.39 X 8.314 X 298/10⁵ = 0.0097 cubic meters.

Since 1 cubic meter is 10⁶ cm³ we can convert the volume to cubic centimeters a more useful unit. It equals 9663 cm³ that is almost 10,000 ml— a lot of volume expansion.

Finally, as far as the kinetics goes, the reaction rate is pretty fast at room conditions, is it not? The kinetics of the reaction will depend on Temperature but unless you go to extremes it may not be critically important.

I assume that when you say you want to "increase the reaction of vinegar and baking soda" you mostly want a reaction that evolves gas faster and maybe more gas. Citric acid actually is a stronger acid than vinegar. You could try substituting the vinegar with a solution of citric acid instead of using the solid acid. You may also want to pay attention to the amounts you are using, aiming for stoichiometric amounts of acid and base to mix. If you want to stick with vinegar, the more concentrated the vinegar, the better.

Another factor that is important, because you are reacting a solid with a liquid, is how fine the solid is. Finer powder means more surface means faster reaction. Mixing speed could also limit your reaction. A safety caution: using a stronger acid than citric acid makes this a lot more dangerous, because a spill of such acid can damage skin, eyes, or clothes.

The vinegar and baking soda reaction consists of the following steps:

1.C₂H₄O₂ --> C₂H₃O₂- + H⁺

2. NaHCO₃ --> Na⁺ + HCO_3-

3. H⁺ + HCO_3- --> H₂CO₃

4. H₂CO₃ --> CO₂ + H₂O

Replacing the acetic acid in step one with a more powerful acid - say, hydrochloric acid (HCl) - will cause the reaction to go faster, as would using a stronger base in steps 2 and 3. However, notice that the ultimate product of the reaction - why it bubbles over - is in step 4, which is not an acid-base reaction: carbon dioxide is insoluble in water, so it bubbles out. As a consequence, whatever base you use would have to be some kind of bicarbonate in order for the reaction to work (it could be a carbonate, too, such as limestone, calcium carbonate, CaCO₃, but that would make the reaction go slower, since step 2 would take much longer).

Raising the temperature will generally raise reaction speed. In this case, it will make step 4 go faster as well, since carbon dioxide, like most gasses, is less soluble in warm water than in cold water.

An interesting link here.