Sure there is nothing wrong with that and lots of affiliates do it.
2 caveats though:
1) Be sure the blog platform you use does not prohibit affiliate links.
2) If you try to join programs and the free blog is the only site you have to show, merchants that do manual reviews may not approve you. But if you apply with your own site that's a good match, then also add a blog even if it's on a free host you should be fine. Lots of merchants though auto approve everyone, so with those programs it would not matter wither way.
One tip is to spend the $8 to get your own domain and email address for your name and put your company info on that site. It just looks more professional and you are more likely to get approved for programs.
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