That depends on your entire itinerary in Japan.
Just to make a roundtrip from Osaka to Kinosaki, you don't need any JR Pass.
A 7-day Ordinary Japan Rail Pass: 28,300 yen.

: What is the cheapest way to travel from Osaka to Kinosaki?

From Osaka Station for example, to travel
via Sasayamaguchi to Fukuchiyama on Fukuchiyama Line,
then to Kinosaki-onsen on San'in (Main) Line.

a. Taking Local and/or Rapid trains: 3,260 yen.
- Fare = 3,260 yen.
- Charge = None.
- Time = about 4 h 15 min.
Osaka dprt., Sasayamaguchi trans., Fukuchiyama trans., Kinosaki-onsen;
07:13 # Local, no transfer , 09:31 - 10:01 Local, 11:28;
10:24 T. Rapid, 11:29 - 11:32 Local, 12:26 - 13:02 Local, 14:36;
12:24 T. Rapid, 13:29 - 13:38 Local, 14:35 - 15:10 Local, 16:42;
13:24 T. Rapid, 14:29 - 14:33 Local, 15:35 - 16:16 Local, 17:44;
# Departure at 07:14 on weekdays;
T. Rapid = Tambaji Rapid.

b. Taking one Ltd. Express train: 4,940 yen to 5,650 yen.
- Fare = 3,260 yen.
- Charge = 1,680 yen (without reservation) to 2,390 yen (reserved seat on a busy-time day).
- Time = about 2 h 45 min.