D.phil /M.phil decision?!

You need to have done a Masters programme to be eligible for a DPhil.

I'm still in a confusion on how to apply for Mphil or Dphil. Can I apply for both? I've planned to apply of Oxford and Kings College can I apply for both the courses in both the Universities?

I'm still in a confusion on how to apply for Mphil or Dphil. Can I apply for both? I've planned to apply of Oxford and Kings College can I apply for both the courses in both the Universities?

As I understand the DPhil is specific to Oxford. It's the same as a PhD elsewhere. My understanding is an MPhil at Oxford (and Cambridge) is different to an MPhil at other universities. At Oxford it's a masters degree, usually a two year course typically with some taught elements (although they may or may not be formally examined) and a significant masters thesis. Outside of Oxbridge, an MPhil is usually just an exit award for a PhD which either was not completed or was deemed to not meet the requirements for award of the doctorate. So if that's the case it's important to be aware of the distinction between them.
I believe at Oxford for many areas it's typical for them to expect a masters degree before entering the DPhil course (which may be at Oxford or elsewhere) although e.g. in STEM subjects this may be more flexible (for humanities subjects I think it'd be rare to go in with just a bachelors). You could likely apply for both the masters and doctorate at Oxford simultaneously although if you already hold a masters then I'm not sure what you would be aiming to get out of doing a second one rather than just proceeding directly to the doctorate. Granted it's possible you could be accepted to a non-funded DPhil and then also applying to the MPhil gives you that option to then reapply to the DPhil for funding but then that's a lot of time and money and there might be better options to then reapply the following year.
Outside of Oxbridge I believe it wouldn't be typical to apply to the MPhil and PhD simultaneously since they are as above essentially the same programme p to the point of being awarded one or the other, as you would typically just apply to the PhD and only be awarded the MPhil if essentially something went wrong (either academically i.e. you were not able to be awarded the PhD, or non-academically e.g. personal/professional circumstances prevented you completing the PhD but they deemed you were eligible for the MPhil award). An MPhil from non-Oxbridge unis may be seen effectively as a "failed" PhD so depending on your goals that might be something you don't want to be aiming for.

If you are applying to the same department for an MPhil and a DPhil it’s likely to raise questions about why, and which course you actually want to do. There’s a huge difference between a Masters and a doctorate. You’d need to explain in your statement of purpose why the course was right for you and it will be assessed by the same panel so look a bit odd for you to write two contrasting statements.
What is is that makes you want to apply for both? What are you hoping to get out of the course?

As I understand the DPhil is specific to Oxford. It's the same as a PhD elsewhere. My understanding is an MPhil at Oxford (and Cambridge) is different to an MPhil at other universities. At Oxford it's a masters degree, usually a two year course typically with some taught elements (although they may or may not be formally examined) and a significant masters thesis. Outside of Oxbridge, an MPhil is usually just an exit award for a PhD which either was not completed or was deemed to not meet the requirements for award of the doctorate. So if that's the case it's important to be aware of the distinction between them.
I believe at Oxford for many areas it's typical for them to expect a masters degree before entering the DPhil course (which may be at Oxford or elsewhere) although e.g. in STEM subjects this may be more flexible (for humanities subjects I think it'd be rare to go in with just a bachelors). You could likely apply for both the masters and doctorate at Oxford simultaneously although if you already hold a masters then I'm not sure what you would be aiming to get out of doing a second one rather than just proceeding directly to the doctorate. Granted it's possible you could be accepted to a non-funded DPhil and then also applying to the MPhil gives you that option to then reapply to the DPhil for funding but then that's a lot of time and money and there might be better options to then reapply the following year.
Outside of Oxbridge I believe it wouldn't be typical to apply to the MPhil and PhD simultaneously since they are as above essentially the same programme p to the point of being awarded one or the other, as you would typically just apply to the PhD and only be awarded the MPhil if essentially something went wrong (either academically i.e. you were not able to be awarded the PhD, or non-academically e.g. personal/professional circumstances prevented you completing the PhD but they deemed you were eligible for the MPhil award). An MPhil from non-Oxbridge unis may be seen effectively as a "failed" PhD so depending on your goals that might be something you don't want to be aiming for.