Is it correct to use the word Klick instead of Kilometer in the following sentences?
It's about 50 klicks to the next gas station.
The US is about 25000 klicks from India by air.
As has been established in this related question, "klick" is a slang word for "kilometer" developed by members of the United States Marine Corps.
It is technically "correct" to use "klick" in place of "kilometer" in those sentences, depending on your audience. However, it's usually not appropriate to use slang or jargon outside of the field or organization it pertains to (in this case, the United States Marine Corps or alied military organizations).
According to Purdue University:
2. In-Group Jargon: Jargon refers to specialized language used by groups of like-minded individuals. Only use in-group jargon when you are writing for members of that group. You should never use jargon for a general audience without first explaining it.
3. Slang and idiomatic expressions: Avoid using slang or idiomatic expressions in general academic writing.
Also, one should be aware that using slang or jargon in spoken English can be tricky. It can be a barrier to successful communication. Slang is, by definition, non-standard (and thus not always widely known), while jargon is often limited to a particular group or context (outside of which, it is largely not understood).
Therefore, unless you're certain the person you're speaking to (or the audience you're writing for) is familiar with a particular term of slang or jargon, it's best not to use it.