One possible solution for either your Kobo or Kindle is to use On-the-Go (OTG) to transfer files from your Android tablet via USB. Most newer Android tablets support this. You just need an OTG USB cable and a file transfer app. I have transferred books from a Nexus-7 tablet to a Kindle this way.
If you plan to send books to a Kindle via your Amazon account it will need connectivity to receive the book. Unless your Kindle has built in 3G cellular service, you will need to be in a location with Wi-Fi or tether from another device (e.g. smart phone).
I do not know of any EPUB to MOBI conversion apps for Android. A trick was recently discovered that allows you to email an EPUB to your Amazon account and have it converted and delivered to a Kindle. You can read more in
this thread. There may be some limitations with this method or it may stop working eventually.
You should be aware that Kindles treat books you have added yourself (known as personal documents) differently from purchased from Amazon. For example in some cases you won't have use of the best typography (kerning and hyphenation) and cover image thumbnails might not be shown. There are workarounds for some of these issues.