Most likely have some RF coming back into the amp. Reflect. Possibly adding some ferrite chokes to the antennas feed point would help with this as well as getting the VSWR readings down as low as possible. Also it could be the variable itself causing the amp to go into oscillation. Not an amp guru, but have heard some not so good things about Fatboy amps. Impedance mismatches and also sub par workmanship. I am not trying to bash the amp maker in any way. May not be the amp. But did you not say you were running a different amp before this one?? If that one was operating correctly then it might very well be the amp having the issues. Also what kind of radio are you using? And export or AM only radio and has it been peaked and tuned??
A clean signal in will help to produce a clean signal out. Not saying your radio is the issue either, just asking so as to try to get as much info as possible. Hope you get it resloved. Pull the amp out of line and see if you can work on getting the VSWR down some more on the antenna. Have you trimmed the whip yet? If not you may want to do this now. Not saying it will cure anything either, but it won't hurt anything. And antenna analyzer would be a great tool at the moment.
Last but not least, you can try the bandage move and try placing the amp away from the radio if it's close. Use different length coax jumpers to VSWR meter and such. Again, just from past experiences this is some of what you might try. Like I said, no amp expert here that is for 110% sure LOL! Just trying to help. There seems to be some issues with the amp, but it's hard to tell at the moment. Post up some pics of the board and you might get some better answers as well. Pics are worth a thousand words!! Might be a wrong part value or something. Ya never know. Again, hope you get it fixed. Be safe and have a good one.