When the price of gasoline/natural gas/oil rises, the shares/dividends of OXY will also rise and more than offset the prices that OXY shareholders have to pay for gasoline or home heating/cooling.
If I understand, the price relation you describe is because of 'inflation'.
As to whether the incremental increase of one price can be offset by the other - that would depend on 1) the amount of gasoline purchased and 2) the number of shares owned.
The CAGR of the dividend payout
The rate of inflation of transport fuels