Combine the feel of classic barre chording with syncopated eighth-note runs for your leads. Build barre chords by laying the index finger across the entire fret. Then add your ring, middle and pinkie fingers to form the relevant chord shape.
Think of barre chords as an extended E shape carried further up the neck--so, for an F barre, you're laying your index finger completely across the first fret, with the remaining three fingers in an E chord shape (first fret, fourth string, followed by your middle and ring fingers on the second fret, second and third strings).
Study photos, videos and interviews to determine Mick's guitar and amplifier setup. Prior to "London Calling," for example, he favored Les Paul Juniors and Mesa Boogie amplifiers. This combination delivered a rich, full sound at peak volumes, yet proved equally suited for cleaner Stax/Volt tones when it was turned down. (For extra wallop, run the Mesa Boogie through a Marshall amplifier cabinet).
Create greater melodic tension with bursts of single-note runs, as exemplified on "All The Young Punks" ("Give 'Em Enough Rope," 1978), or the outro of "Clash City Rockers," which is basically an extended E to D jam ("The Clash," 1977).
Spice up those classic Morse code-style leads with a judicious bend of the string. Just make sure that your finger carries the greater load; it'll be easier on your wrist!
Note the chords and scales that Jones favors--early Clash material bears the imprint of '60s Mod bands like the Who or the Kinks (as any comparison of "1977" and "All Day And All of The Night" shows). Even toward the end of his tenure, Mick remained something of a traditionalist (as in "Should I Stay Or Should I Go," built on a classic Who-like D-G-A-D sequence).
Study early Clash albums to get a sense of Mick's interplay with lead singer/rhythm guitarist Joe Strummer (who favored the Fender Telecaster). Not surprisingly, the reinventor of the E-D-A-G progression isn't prone to using many minor chords, which do appear as punctuation in unexpected places (such as "Lost In The Supermarket."
Don't be afraid to take other styles on board. Compare the rock and reggae mixture on "White Man In Hammersmith Palais" with Jones' current Carbon/Silicon material, and you'll realize what's been the sole constant throughout his three decades of playing music.