Hi there!
The only rail pass that will cover this trip would be a 14 day Japan Rail Pass. Lets quickly take a look at the costs of your trip to see if it will be cheaper than purchasing tickets (I'll assume you start your rail pass from Osaka, but depart from Kansai Airport):
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Osaka > Hiroshima: ¥10,220 (109mins, 345km)
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Hiroshima > Toyooka(hyogo): ¥9,540 (276mins, 345km)
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Toyooka(hyogo) > Kyoto: ¥4,390 (146mins, 148km)
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Kyoto > Tokyo: ¥13,020 (164mins, 513km)
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Tokyo > Odawara: ¥3,440 (35mins, 83km)
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Odawara > Osaka: ¥12,270 (159mins, 472km)
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Osaka > Kansai airport: ¥3,340 (57mins, 64km)
JR ticket cost: ¥56,220 for 7 legs
As you can see a 14 day pass will give you good savings and you will also have the flexibility to use the any further JR lines for free during the 14 day period (eg, in Tokyo).
Hiroshima to Toyooka will be very feasible - I recommend travelling to Kyoto on the bullet train and then transferring to a Kinosaki ltd express) for the trip to Toyooka. Also, please note that actually the majority of your travel will be on bullet trains so you will have a lot of time at high speed!
I hope this helps!