Is the name "Skylr" a masculine name?

If you're unsure of a name I'd recommend Googling it. It may bring up meanings or connections you hadn't thought of.

Re your actual question, I'd say it's a name that can be used for men and women. However, if I was trans I'd personally want a name that was clearly male or female. Without knowing your personality it's impossible to advise best.

Take your time choosing.

I have met guys and girls named Skylr, with many different spellings. The girls tend to have a 'e' in it while the guys have it as you have written it. Honestly, I wouldn't be thinking on how the name sounds but more on how you present yourself. Do you want to be a feminine guy or a masculine guy? Portray yourself as how that name should, if you believe the name is masculine act more masculine, but stay true to yourself. The main thing is if your new name doesn't match your personality, it's kind of funky and the chance of people calling you your pre-transition name becomes higher. And for me that is the most degrading thing I have ever experienced.