What evidence is there from scripture for why Daniel did not eat the King's food?

The issue is not so simple that the meat was from unclean animals. Daniel and friends could help themselves to only the clean animals.

The issue should not the about slaughter and preparation. We must not read current practices back into the text. There was no Kosher certification then. The only requirement was the exsanguination of the animal, which we can suppose was the common way to kill animals even for non-Jews.

We are not told why. But it would be apparent to Daniel and friends. We can only conjecture.

1. The meat of clean and unclean animals were mixed in such a way that they could not distinguish them.

2. The Babylonians did not kill by exsanguination (not likely).

3. All the animals were sacrificed to idols, at least in a token way. For example. All Muslim Halal slaughtered animals are prayed over with the Muslim prayer.

I think #3 is more likely.

Whatever reason we suppose, we need to observe that the young men were open to other aspects that amounted to deculturalization for them. New language, new subjects, new identity (name), with Daniel being named after their god "Bel." Yet this was the area in which they pushed back.

I like to also ask how Daniel could have gained the favor of Ashpenaz from the first day. What were they eating before this? Prisoners in exile don't usually get to choose their food.

I don't see this as a redline that these young men drew. It seems likely likely they had to do whatever they had to do to survive. But at the earliest opportunity, they chose to be true to God's commands. To me it seems more like a story of persevering and not giving up on doing that is right under adverse circumstances.

Daniel 1:3-5 explains how some of the young men from Judah’s royal family and the nobility were taken captive and were to be trained for three years then they would enter into the service of King Nebuchadnezzar. They were assigned a daily amount of food and wine from the king’s table. The reason why Daniel refused to eat this food and drink this wine is given in the NIV Study Bible notes:

“Israelites considered food from Nebuchadnezzar’s table to be contaminated because the first portion of it was offered to idols. Likewise a portion of the wine was was poured out on a pagan alter. Ceremonially unclean animals were used and were neither slaughtered nor prepared according to the regulations of the law.”

By providing food and drink from his own kitchens, King Nebuchadnezzar was trying to create a bond of dependence, gratitude and loyalty from the captives, but Daniel and his compatriots were having none of it. The NLT Study Bible comments that Daniel and his friends were not going to yield their religious and moral independence to the king.

The fact that they appeared more healthy after the ten days was a beneficial result, but was not the reason for abstaining from the food and drink prepared in King Nebuchadnezzar's kitchens. Their absitnance was based on remaining true to God's instructions.

EDIT: After the flood God told Noah that everything that lives and moves could be eaten as food - this in addition to green plants (Genesis 9:2-4). So Daniel and his companions were at liberty to eat meat. What they couldn’t eat, however, was meat that had not had the lifeblood drained out of it or meat that had been sacrificed to idols. In pagan Babylon, ceremonially unclean animals were eaten and were neither slaughtered nor prepared according to the regulations of the Mosaic Law. That is why Daniel and his companions refused to eat the food from Nebuchadnezzar’s table – they were not prepared to break the Mosaic dietary laws. This was an issue of obedience to God’s laws.

Daniel said to the guard who had been appointed over himself and his three companions ‘Please test your servants for ten days: Give us nothing but vegetables to eat and water to drink. Then compare our appearance with that of the young men who eat the royal food, and treat your servants in accordance with what you see.’ So he agreed to this and tested them for ten days” (Daniel 1:8-14). Clearly, this rather stringent diet did not harm them physically or mentally, but to claim that it was the diet that was responsible for wisdom and understanding dreams is to deny the power and will of God in the events that unfolded.

Take the example of Joseph, who was sold into slavery and imprisoned because he refused to sleep with his master’s wife. In Genesis 40, Joseph correctly interpreted the dreams of two of Pharaoh’s servants. Later, Joseph interpreted the king’s dreams. Was the ability to interpret dreams as a direct result of Joseph being on a prison diet of bread and water? Was it Joseph who took the credit for dream interpretation? Of course not! It was God who gave Joseph (and Daniel) the interpretations.

There are two primary, though related reasons for why Daniel would not eat the king's food and drink.

Daniel was an Israelite (Dan 1:3) of the tribe of Judah (Dan 1:6). He would be bound by the dietary laws regarding clean and unclean foods (see commands for example at Lev 11:46-47). As well, there was preparation and cooking instructions to be followed. Daniel had no control over these things as regards the food, but only the vegetables and water.

The other reason is that most likely the king's food would have been offered to idols before eating. This too was not permitted.

It was the custom to throw a small part of the viands and wine upon the earth, as an initiatory offering to the gods, so as to consecrate to them the whole entertainment (compare Deu 32:38 ). -Fausset-

So, the evidence from scripture about why Daniel will not eat basically boils down to it was against their Covenant.