1-chloroethanol isn't stable. It will decompose into acetaldehyde and HCl. You might be able to produce fleeting amounts of it in the gas phase, but it probably wouldn't stick around long enough to measure the pKa.
For what it's worth, 2-flouroethanol is only moderately more acidic than ethanol (pKas of 14.42 and 15.18, respectively).
