Which Low Input Current Buffer Chip?
Check out the electrical characteristics in the datasheet- normally close to the back, so almost 200 pages in. 

You will find that the output levels are guaranteed for relatively high currents, more than enough to drive a ULN2003A. 

Although some datasheets brag about drive levels in the large print near the front, it's always advisable to read the fine print, if only to find out how well they actually drive that current (minimum output voltage when sourcing current, maximum when sinking).