I can't say I see a direct connection between Kant and Nietzsche. I was under the impression Nietzsche's most direct influence was Schopenhauer, but I also have a lot to learn about Nietzsche.
I have reached the point where I see philosophy and science as actually complimentary, especially in the big picture scientific disciplines like cosmology and abiogenesis.
Philosophy and science were not even considered separate disciplines until the 19th century.
My favorite current scientist is Sean Carrol, who has dual degrees in philosophy and theoretical physics - he is a philosophically-thinking scientist. As was Albert Einstein for that matter.
Scientists are not trained in formal logic. Philosophers are. Philosophers can help scientists understand what counts as a good explanation, and with their training in ontology and epistemology, philosophers are more directly concerned with finding the limits of knowlege and with how good our purported knowlege actually is. They are good at helping scientists refine the explanatory power of their theories.
For the most part, scientists are interested in fitting the data to theories. If the data can be fit, and experiments can be replicated, they view their job as essentially being done. That approach may, or may not be an accurate reflection of an underlying truth about objective reality.