「Verb in て-Form + しまう + 見込{みこ}みです」

While I would not consider this expression incorrect per se, I know for certain that it would be far less common than:

「Verb in Dictionary Form + 見込{みこ}みです」 used in conjunction with a phrase expressing disappointment.

You could say, for instance:

「残念{ざんねん}ですが、電車{でんしゃ}が遅{おく}れる見込みです。」 or

「電車が遅れる見込みだと聞{き}いて残念です。」

Finally, if you must use 「しまう」 for some reason and still want to sound perfectly natural, you could use it by changing 「見込み」 to 「可能性{かのうせい}」. I know this might not be what you wanted to know, but for future reference, I added it.

「Verb in て-Form + しまう + 見込{みこ}みです」

While I would not consider this expression incorrect per se, I know for certain that it would be far less common than:

「Verb in Dictionary Form + 見込{みこ}みです」 used in conjunction with a phrase expressing disappointment.

You could say, for instance:

「残念{ざんねん}ですが、電車{でんしゃ}が遅{おく}れる見込みです。」 or

「電車が遅れる見込みだと聞{き}いて残念です。」

If you must, however, use 「しまう」 for some reason and still want to sound perfectly natural, you could use it by changing 「見込みです」 to 「可能性{かのうせい}があります」. I know this might not be what you wanted to know, but for future reference, I added it.

「電車が遅れてしまう可能性があります。」