Heat rate is a scalar quantity, while heat flux is a vectorial quantity. To define the heat flux at a certain point in space, one takes the limiting case where the size of the surface becomes infinitesimally small.
Heat Flux Density Converter  

Solution:
BTU/hour square foot = 66360.42984099999
BTU/minute square foot = 1106.007164836955
calorie/second square centimeter = 5
dyne/hour centimeter = 753624000001.6965
erg/hour square millimeter = 7536240000.016965
foot pound/minute square foot = 860660.7879943552
gram calorie/hour square centimeter = 17999.99999879024
horsepower (metric)/square foot = 26.442359541914602
horsepower (UK)/square foot = 26.08062992958372
CHU/hour square foot = 36866.90548278824
joule/second square meter = 209340.00000078825
Kilocalorie/hour square foot = 16722.547192856655
kilocalorie/hour square meter = 180000.00000059672
kilowatt/square meter = 209.34000000078822
watt/square centimeter = 20.93400000007882
watt/square inch = 135.05779430146677
watt/square meter = 209340.00000078825