Depending on your application (are you developing pre vs post flow amounts off your site) we typically use the conservative approach and assume that in pre development any drainage area flowing to a sinkhole is completely ignored (no outflow). Therefore, you are lowering your pre developed flow offsite and this keeps your post developed allowable flow offsite to a minimum. If it truely is a sinkhole then infiltration rates are difficult to measure and will be at an ever changing rate as silt clogs the infiltration routes.
We have created storm water injection wells in sinkholes by excavating to the open throat and grouting in a vertical perforated large diameter HDPE pipe and backfilling with 1 foot layers of graded stone separated by a geosynthetic material. In the end the volume of the sinkhole had to be large enough to accomodate the 100-yr, 24-hr storm event runoff amount without overtopping while still assuming no outflow for the same reasons listed above.
An exception we have ran across is when the sinkhole was located close enough to a federally governed body of water such as a lake or river and this governing agency (TVA) had posted flood elevations around the sinkhole on FEMA maps. They had in the past performed dye tests to show that the sink was directly connected to the lake. This superceded the local governments authority and regulations on land improvements involving a sinkhole's watershed.