Kindle Fire HD (Tate) boot loop, after attempt to install CM I attempted to install Cyanogenmod on my Tate, according to the directions in the Wiki.

https://wiki.cyanogenmod.org/w/Install_CM_for_tate

At Step 3, number 5 (fastboot -i 0x1949 oem recovery), the kindle does not boot to recovery, but just shows the logo, and then goes back to Fastboot, even with a non-fastboot cable.

If I restart without a cable attached, I get a boot loop (even when I hold down the volume button, as described).

Perhaps this is relevant: before I started all of this, my Tate was already rooted. Was it stupid to apply the exploit in that case? I only realized this later. If so, is there any way out?

BTW, I'm on Linux, have a working adb and a fastboot cable.

Thanks!
Got it! 

I did re-flash the recovery, and that seemed to take care of it. 

Before that, I also went 

fastboot -i 0x1949 oem idme bootmode 4000

However, that took a while but then said it failed, so maybe just re-flashing the recovery by itself was what did it.