¿Can you believe in an old earth and a global flood?

Probably not. The earth is old, and there are local floods all the time, so those two are definitely not contradictory.

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Spare a thought for the stay-at-home voter;
His empty eyes gaze at strange beauty shows
And a parade of the gray suited grafters:
A choice of cancer or polio. -- The Rolling Stones

I'm sure that there were local floods 4500 years ago. Do you think that heavy rainfall wouldn't have caused rivers to overflow into the flood plains 4500 years ago?

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Spare a thought for the stay-at-home voter;
His empty eyes gaze at strange beauty shows
And a parade of the gray suited grafters:
A choice of cancer or polio. -- The Rolling Stones

Actually, the two are pretty independent concepts. Either the earth is old, or it is young. In either case, either there was a local global flood in historical times, or there wasn't.The main reason that young earth/global flood are linked is because Biblical literalists insist that because Genesis describes both, they must both be reality. (Also, literalists seem to believe that a global flood will explain data that indicates an old earth, but that's not correct.) But young earth and global flood will each, by themselves, independently, be confirmed or be contradicted by the different data.

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Spare a thought for the stay-at-home voter;
His empty eyes gaze at strange beauty shows
And a parade of the gray suited grafters:
A choice of cancer or polio. -- The Rolling Stones