the most "similar" bands to Jefferson Airplane i can think of off the cuff are Sweetwater (lighter and more jazz-influenced, but with a lot of similarities and a leading lady with LUNG POWER!!) and H.P. Lovecraft (who actually opened for Jefferson Airplane a few times). H.P. Lovecraft -- the band, not the author for whom they are named -- are difficult to track down, but SO worth it. the kind of represen the trippier more apocalyptic aspect of JA (think more along the lines of After Bathing at Baxter's and Crown of Creation) wheras Sweetwater's the one you want to check out if you're into the lighter more carefree aspect (think Surrealistic Pillow).
oh... and if you like the Kinks, be sure to check out The Standells, The Blues Magoos, and The Count Five.