Is my boss flirting with me?

THIS IS A BIT LONG BUT GUYS, BEAR WITH ME. I HAVE TO GIVE AS MANY EXAMPLES AS POSSIBLE SO YOU CAN TELL ME.

Hi I am 25 years old and work at an accounting firm. I have recently noticed that boss in our dept who is 45 may be flirting with me at work. I have been there for several months now. I know that dating anyone from work could get messy but I think I feel flattered by all of this behavior.
The boss is an overall friendly person with people and mellow. However, in the beginning I thought it was just being nice to me like he is with most people there, but I am starting to think it may be flirting.
For example, one day I wore a pretty white dress and he told me during lunch as he walked passed me "you look really great today." Then we spoke over the phone from my cubicle and I asked a question about paperwork and he said, "By the way you look really, really, nice today, and your hair is amazing."
Also, I asked for some supplies to be sent to my cubicle, which may have usually taken a day at least to get, but he personally brought them over. He also told me "you look like a model," and gave a friendly invite to lunch when we were going to be in the same city last month for vacation. I ended up not going on vacation at all thought so that never happened.

Other things are him saying that he feels like leaving the company because of the stress and commuting into the city and I said, "If you leave, so will I," in a friendly tone. I only said this bc the other bosses are arrogant and hard to deal with. He answered, "I will let you know where I will be so you can follow me." He has also promised me a promotion in a higher dept. for next winter and mentioned it again out of the blue yesterday with a smile. This morning he asked me if I was going to go to the companies "Beginning of Summer," bash at a catering hall. Why would he ask?

One day I also called his office for a question about work and he said, "I am glad you called me. I had an annoying caller on line 1 and you saved me."

Do you think the comment "follow me," and asking about the bash are flirting?

I would be interested in getting to know the person but don't want to send out signals if this is just a "friendly" approach. This is why I asked if he seems to be flirting. I get confused about it. It is a delicate situation at work and I don't want to say something flirtatious and look bad.
Today, everyone in the office was busy. However, there was eye contact made when I went to clock in. Then I was in a coworkers office to print something, he passed by from outside and from a few people in there his eye contact falls right onto mine-twice. The third time was in the hallway from like 30 feet down the hall, he was talking to someone and it's as if he noticed me from the corner of his eye and looked up in my direction. Does this also show interest?

Today he made a comment when I went into his office to hand in some papers. I was wearing a cute red pencil dress and he looked at me checking out my outfit saying "You look....very Latin today." (My background is from Argentina and Spain). He did a quick up and down scan with his eyes. I don't know what to say. I also asked him how the annual bash was and he said "it was OK." I asked if I skipped out on a fantastic time, and he said "no, don't worry, I would have let you know."

Yesterday, he called my cubicle to tell me that he was impressed with my french. he is French Canadian and I studied it for years, so I wrote an email about some clients all in french and he seemed to be impressed. He said, "I am very impressed with all of these qualities, you are some dream girl!" Then I had to work 5 floors up in another office and he took the stairs to come up and see if I was there. I am leaving for vacation in two days and he peeked in the office door and said, don't forget to pass by and say goodbye when you leave." Someone else was in the office and gave a weird look with a smirk-maybe I was being paranoid or maybe he picked up on something. I then called the boss when the other person left and asked, "did you need me for something?" he said "no, I just came by to see you and I took the stairs too (not the elevator)." He also knows some guy likes me in the building and sort of follows me around, he said, "that's what happens when you're gorgeous."

Today was weird, a coworker and friend of mine went by his office before leaving but he was acting different-,meaning not as "friendly". There were a few other people around who work there. He also said he had a headache. I don't know what to think. He seemed a bit of in a rush, but it was the end of the day. He walked us out and down the block though.

All this confuses me, really. I will be back at work in a couple of weeks.

What vibes should I send out and how can I flirt back without making things uncomfortable. After all, it is a workplace. Because of days like today, this is why I don't know if he likes me.

to be honest, you are in the best position to judge, what kind of person is he? some guys are just friendly all the time and since you are still fairly new there (i am an accountant too, it took me a while to get comfortable with the people at work) he might be trying to make you feel welcome. But then again commenting on the way you look (and repeatedly) would indicate some sort of attraction and to me anyway does not seem to be normal office conversation, i would say based on the examples you gave, he does like you, i know my bosses dont talk to the female staff like that, especially new staff

i would have to warn you about relationships in the workplace, especially with a boss, we are talking about your livelyhood here, if it goes sour, chances are you will get screwed (figuratively speaking of course), money comes first imo, you still have a long career ahead of you, this might not be the best way to start it, all of this is my opinion, take it or leave it

It does not sound like major flirting, but if you are uncomfortable with some comments after all it is the workplace. Explain that to him, don't make it worse and try any flirting back.

He probably does like you, but is he married? That changes the whole situation. 45, accounting firm, high on the 'ladder' I'm guessing he is married.

Nothing inappropriate has transpired, but it does seem that he's a bit flirty.

If he's single, you can date him, but only if you're willing to risk your job over it. if the relationship goes south, you'll find yourself wanting to go to hell rather than go to work.

do you like it or not? this is the major question. If not, you should stay away from him and keeps a distance, else he missunderstands you