If it programs the chip and the chip works, then you should do the following.

1) First of all, carefully check all the connections of U2 chip.

2) Try to read the signature bytes. If it works then LS299 is fine.

3) If not, then try using HC299 chip. This IC is used in the programmer for read back function in order to verify the flash.

4) Also use a short connecting cable from programmer to PC.

I hope this should solve the problem. I also built this programmer and it works fine.