I tried to simplify the code a bit for my sake. I think there is still a problem with double and single quotes.

DECLARE @cmd VARCHAR(2048)
DECLARE @FileName VARCHAR(500)

SET @FileName="PatientFile_" + CONVERT(VARCHAR(30),GETDATE(),112)

SET @cmd = 'bcp "EXEC SigHealth..spRadialAnalyticsDataExtract_PatientFile" queryout' +' "\\xx-sftp\dddd$\RadAns\"' + @FileName + ".txt"  -c -T -t,' +' -SLOCALHOST" '
print @cmd
EXEC master..xp_cmdshell @cmd, NO_OUTPUT