I run 700 X 23c Armadillo All Condition tires on one of my fixed. Havn't had a flay in over 1000 miles.
On my other fixed I run 700 X 23 Michelin Race pro. The pros are faster but not as much flat protection.
The response of the Armadillo tires are a bit slugish but I am willing to cope with it for the flat protection.
Tony