Q.Do I mix Neem Oil with a cooking oil or just water?
want to use Neem Oil on flowers.

Mix with water, not cooking oil.
Follow the mixing instructions on the product label. If you are using 70% neem oil, the rate is one ounce per gallon of water. No spreader/sticker needed.
And note the Precautionary Statements and Environmental Hazards. Just because a biopesticide is organic program compatible, it doesn't mean it is without some degree of hazard for the applicator and the enviroment.
Mixing Instructions:
Mix 70% NEEM OIL at the rate of 2 tablespoons (1 fluid ounce) per gallon of water. Thoroughly mix solution and spray all plant surfaces (including undersides of leaves) until completely wet. Frequently mix solution as you spray.
PRECAUTIONARY STATEMENTS HAZARDS TO HUMANS AND DOMESTIC ANIMALS CAUTION: Causes moderate eye irritation. Harmful if absorbed through skin. Avoid contact with skin, eyes, or clothing. Wash thoroughly with soap and water after handling and before eating, drinking, chewing gum, or using tobacco. Remove and wash contaminated clothing before reuse.
ENVIRONMENTAL HAZARDS To protect the environment, do not allow pesticide to enter or run off into storm drains, drainage ditches, gutters or surface waters. Applying this product in calm weather when rain is not predicted for the next 24 hours will help to ensure that wind or rain does not blow or wash pesticide off the treatment area. Rinsing application equipment over the treated area will help avoid run off to water bodies or drainage systems.
BEE HAZARD This product is toxic to bees exposed to direct treatment. Do not apply this product while bees are actively visiting the treatment area.