Can I use Oracle DB EE and Oracle Goldengate for YouTube blog?

No one in this forum can give you information about licensing on behalf of Oracle. Besides, what license you have? For info about the developer license that may apply when downloading software from Oracle, see the following URL:

https://www.oracle.com/downloads/licenses/standard-license.html

Are there any other blogs that use Oracle in a similar fashion as you plan to do? That may give you some idea. My understanding is that the developer license allows you to use the software for the purpose of demonstration.