Is your car a manual or auto? If I read what you posted correctly, you installed the konis and the clunking started. Could be the konis that are causing the noise and issue. Other people I've known that have konis as well report similar issues.
Otherwise if you have a manual, that noise would be normal when you're engaging/disengaging the clutch and shifting gears. Mustangs do make a lot of noise.
2014 GT - Track Pack, Leather Recaros, Electronics Package, Back-up Camera - Ported CJ Manifold, SCJ Mono-Blade TB, Custom Intake, Kooks 1-3/4" LT's, Kooks O/R H-pipe, Borla S-Types, AED Tuned - 443 RWHP / 388 RWTQ
Ordered: 3/19/2014 - Built: 5/13/2014 - Delivered: 5/19/2014