I am new here. Recently I bought a K1000 and want to use a Fiio A1 to drive it. I am not sure will this works. Any advice will be appreciated.
I have used several different Class D amplifiers with my K1000's and found them to work very well. While I have not used the Fiio A1, based on it's specifications, I can see no reason why it would not work well with your K1K's.
Much depends upon the quality of the power supply used with Class D amps. I would consider using a 12v battery pack with a quality charger, as it would be a simple DIY project that should yield significant improvement to the performance of the A1.
Like Ron (HiFlight) I too have listened to K1000 using various Class D amps with excellent results. Another option would be a 1970's vintage receiver by Marantz/Pioneer/Technics in the 15-45 wpc to drive your K1000 via a pigtail (speaker to 4-Pin plug). Good luck.