Playing 2 Amps (A/B Box & Chaining)
When connecting two amps together, the best solution for tone and usability is an A/B Box. You can choose to play through one amp (A), the other amp (B), or both (AB) at the same time. If "A" is your more distorted amp, it can be used as your main blues harp sound. If "B" is your cleaner amp, it can be used for the songs where you want a cleaner sound. When you need a lot of volume (band gets loud... or you just need some boost for a powerful section of a song), then use both "A" and "B" at the same time. This is usually achieved by using two different models of amps, though if you have two new amps, such as the Fender Super Champ X2 I mentioned yesterday, you could set one amp to the clean channel and one to the distortion channel to achieve this difference in tone.
If you use an A/B box with optical switching, such as the Whirlwind Selector A/B Box (http://www.musiciansfriend.com/amplifiers-effects/whirlwind-selector-a-b...), you won't have any audible "clicks" when switching from amp to amp. Some pedals that use analog switching are fine as well, though I recommend you try them in person, I have heard some that have audible clicks that are not acceptable.
If you have a classic amp with two inputs for the same channel (such as the Fender Bassman), then you can omit the use of the A/B Box by plugging your mic into Input 1 and running an instrument cable from Input 2 to the other amp (Input 1 and Input 2 in classic amps are commonly joined internally). Not all amps are wired this way and sometimes an undesirable tone is produced from one amp or both, so experiment with this first my playing through amp 1 directly, then amp 2 directly, and then chaining them together and listening carefully for any change in tone. Again, an A/B Box is the safest bet.