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Given that I have an irregular object image (flower) and I am only allowed to use 30 percent of the image/page with said object is there a way to tell this in photoshop or any other program? I just need to make sure the flower pixels add up to 30 percent of the total pixels on the page.

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It depends whether you can separate the background from the foreground (which is your flower) with some thresholding filter or by automatic or manual selection.

When you can use the magic wand tool or another selection method to surround your flower, getting the pixel count is very easy. Take for instance this flower

enter image description here

With the magic wand, I can easily select the white background with a simple click

enter image description here

The rest is easy. Open the Histogram, click on the small context menu in the upper right corner of the histogram window and open the detailed view. This shows the number of pixels in the current selection which is about 80700. When you remove the selection you see in the very same spot the pixel count of the complete image which is 120000. Therefore, the background takes 80700/120000 = 0.67 = 67% of the image.

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Divide the amount of pixels in the flower by the amount of pixels on the page then x 100 (to get the total amount of pixels of each multiply the width and the height.)

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