You don't mention what type of roof you have, the age or if the kitchen roof is connected to the rest of the house.
I am thinking that you probably have tar and gravel on your flat roof.
If it is ten or more years old. It would be a good idea to do a tear off and check to see if any or all of the sub-roof needs replacing.
Since you are asking for advice on how to repair it yourself, I am assuming that you don't want to hire a roofing company.
If your roof is tar and gravel, you can scrape it off with a flat edged shovel, (it is a lot of work), but once you have the old top portion off, check to see if any of the plywood sub-roof needs replacing. (You'll need a janitors broom to sweep the sub-roof off with, to clear any loose bits of gravel off). If you see any deterioration in the sub-roof, replace those pieces, then you can lay felt paper, but you will need to overlap the felt at least 8 inches per line. Make sure to over lap the same where each roll ends. You will need to pop some lines in order to keep your paper straight, so pick up a chalk line and powder.
You will need a bucket of Simplex nails, (small nails with round plastic heads on them).
Once you have the tar paper,(felt), down, nail the simplex over all the edge lines of the felt where you have overlapped the paper, about two inches apart, with the simplex nails. Including the end of roll overlaps.
You will then need to lay down some bull pitch, (black tar). I would use the (wet or dry plastic type). You'll need several buckets, depending on the size of your roof. I recommend; (gardner- Wet-R-Dri All Weather Plastic Roof Cement.
Thourougly apply the bull over the tar paper in strips as you lay the rolled roofing over top of the paper. Making sure to cover the simplex nails really well. Do NOT use tar/pitch sparingly and make sure it is spread well on each edge of the felt paper.
You can use a paint roller with a long painters handle on it to roll the tar onto the roof.
You'll need a razor knife and plenty of sharp blades to trim the edges with along the edge of the roof line. Wait for the tar to set up before trimming the edges.
Total cost in materials will depend on the size of the roof.
It is difficult to find a leak on a flat roof and try to patch it with tar, but if you feel the task of replacing the kitchen roof is too much, and you can't afford a roofer, than you could try to locate and patch it with tar/bull roof cement.
You can pick up everything you need to get the job done, at a local supply store such as; The Home Depot.
I like rolled rubber roofing on flat roofs. It is easy to install and, compared to other roofing materials, is less likely to leak.
Is your entire home a flat roof? If not, and the flat roof is joined to a sloped roof, you could have water coming in under the shingled part of the roof, and running under the flat roofing. You need to get a professional to look at your roof. I was a roofer for several years. Got out because of back problems. Water will always seek the lowest point. It could be running onto your flat roof from deteriorated shingles. At any rate, it would be impossible to tell what is wrong with it without looking at it. Generally, just pouring on tar has never helped me, especially if you have gravel on the roof. You may not even cover the crack if you can't see it for the gravel. A comparatively inexpensive fix is rolled roofing. It''s easy to install, at least for someone that's done it before. You should be able to find something about installing rolled asphalt roofing products online, or at your local do it center so you can see if it 's something someone in your family might be up to doing.
Hallo please tell me how to mend my flat roof
You can easily repair your roof leak. First of all you need to find out the leaks from the upper part of the roof. Just go to the roof and point out all the leaks in your roof. So by identifying the roof leak you will be able to repair them so that you can easily fill those leaks. So when you have identified the roof leaks just make sure that the material of the roof are not so damaged so that It can not be repaired. So when you are sure about the material you can repair the roof leaks. There are two ways you can try in order to repair the roof leak one way is used if the roof leaks are so small even glue which has potential to fill those leaks easily so you can try those roof leaks.
So just fill the holes with the glue and place some hard materials in the holes so that I does not leak any more. Once the glue will which you have put in your roof is dry then it will support the roof and the roof will not leak later. But if the roof leaks are large and you need to repair them with some hard material.
A good solution is to cover the whole roof with tiles (cement).
Just call a roofer, and have them retar it, have it hot mopped. This will do the job as long as there isn't too much rotting going on in the roof. Hope this helps, good luck to you.